In 53 60, use a graphing utility to graph each function

The interval (2, 5) can be written as the inequality ___________.

The slope of the line containing the points (-2, 3) and (3, 8) is ________. (pp. 2930)

Test the equation y = 5x2 - 1 for symmetry with respect to the x-axis, the y-axis, and the origin.

Write the pointslope form of the line with slope 5 containing the point (3, -2).

The intercepts of the equation y = x2 - 9 are ______________________. (pp. 1819)

A function f is ___________ on an open interval I if, for any choice of x1 and x2 in I, with x1 6 x2 , we have f1x12 6 f1x22.

A(n) function f is one for which f1 -x2 = f1x2 for every x in the domain of f; a(n) ________ function f is one for which f1 -x2 = -f1x2 for every x in the domain of f.

A function f is decreasing on an open interval I if, for any choice of x1 and x2 in I, with x1 6 x2 , we have f1x12 7 f1x22.

A function f has a local maximum at c if there is an open interval I containing c so that for all x in I, f1x2 f1c2.

Even functions have graphs that are symmetric with respect to the origin.

In Problems 1120, use the graph of the function f given.Is f increasing on the interval (-8, -2)?

In Problems 1120, use the graph of the function f given. Is f decreasing on the interval (-8, -4)? Is f decreasing on the interval (-8, -4)?

In Problems 1120, use the graph of the function f given.Is f increasing on the interval (2, 10)?

In Problems 1120, use the graph of the function f given.Is f decreasing on the interval (2, 5)?

In Problems 1120, use the graph of the function f given.List the interval(s) on which f is increasing.

In Problems 1120, use the graph of the function f given.List the interval(s) on which f is decreasing.

In Problems 1120, use the graph of the function f given.Is there a local maximum value at 2? If yes, what is it?

In Problems 1120, use the graph of the function f given.Is there a local maximum value at 5? If yes, what is it?

In Problems 1120, use the graph of the function f given.List the number(s) at which f has a local maximum. What are the local maximum values?

In Problems 1120, use the graph of the function f given.List the number(s) at which f has a local minimum. What are the local minimum values?

In Problems 2128, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which it is increasing, decreasing, or constant (d) Whether it is even, odd, or neither

In Problems 2128, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which it is increasing, decreasing, or constant (d) Whether it is even, odd, or neither

In Problems 2128, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which it is increasing, decreasing, or constant (d) Whether it is even, odd, or neither

In Problems 2128, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which it is increasing, decreasing, or constant (d) Whether it is even, odd, or neither

In Problems 2128, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which it is increasing, decreasing, or constant (d) Whether it is even, odd, or neither

In Problems 2128, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which it is increasing, decreasing, or constant (d) Whether it is even, odd, or neither

In Problems 2128, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which it is increasing, decreasing, or constant (d) Whether it is even, odd, or neither

In Problems 2128, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which it is increasing, decreasing, or constant (d) Whether it is even, odd, or neither

In Problems 29 32, the graph of a function f is given. Use the graph to find: (a) The numbers, if any, at which f has a local maximum value. What are the local maximum values? (b) The numbers, if any, at which f has a local minimum value. What are the local minimum values?

In Problems 29 32, the graph of a function f is given. Use the graph to find: (a) The numbers, if any, at which f has a local maximum value. What are the local maximum values? (b) The numbers, if any, at which f has a local minimum value. What are the local minimum values?

In Problems 29 32, the graph of a function f is given. Use the graph to find: (a) The numbers, if any, at which f has a local maximum value. What are the local maximum values? (b) The numbers, if any, at which f has a local minimum value. What are the local minimum values?

In Problems 29 32, the graph of a function f is given. Use the graph to find: (a) The numbers, if any, at which f has a local maximum value. What are the local maximum values? (b) The numbers, if any, at which f has a local minimum value. What are the local minimum values?

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 33 44, determine algebraically whether each function is even, odd, or neither.

In Problems 4552, for each graph of a function y = f1x2, find the absolute maximum and the absolute minimum, if they exist.

In Problems 4552, for each graph of a function y = f1x2, find the absolute maximum and the absolute minimum, if they exist.

In Problems 4552, for each graph of a function y = f1x2, find the absolute maximum and the absolute minimum, if they exist.

In Problems 4552, for each graph of a function y = f1x2, find the absolute maximum and the absolute minimum, if they exist.

In Problems 4552, for each graph of a function y = f1x2, find the absolute maximum and the absolute minimum, if they exist.

In Problems 4552, for each graph of a function y = f1x2, find the absolute maximum and the absolute minimum, if they exist.

In Problems 4552, for each graph of a function y = f1x2, find the absolute maximum and the absolute minimum, if they exist.

In Problems 4552, for each graph of a function y = f1x2, find the absolute maximum and the absolute minimum, if they exist.

In Problems 53 60, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

In Problems 53 60, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

In Problems 53 60, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

In Problems 53 60, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

In Problems 53 60, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

In Problems 53 60, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

In Problems 53 60, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

In Problems 53 60, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.

Find the average rate of change of f1x2 = -2x2 + 4 (a) From 0 to 2 (b) From 1 to 3 (c) From 1 to 4

Find the average rate of change of f1x2 = -2x2 + 4 (a) From 0 to 2 (b) From 1 to 3 (c) From 1 to 4

Find the average rate of change of g1x2 = x3 - 2x + 1 (a) From -3 to -2 (b) From -1 to 1 (c) From 1 to 3

Find the average rate of change of h1x2 = x2 - 2x + 3 (a) From -1 to 1 (b) From 0 to 2 (c) From 2 to 5

f1x2 = 5x - 2 (a) Find the average rate of change from 1 to 3. (b) Find an equation of the secant line containing 11, f1122 and 13, f1322

f1x2 = -4x + 1 (a) Find the average rate of change from 2 to 5. (b) Find an equation of the secant line containing 12, f1222 and 15, f1522.

g(x) = x2 - 2 (a) Find the average rate of change from -2 to 1. (b) Find an equation of the secant line containing (-2, g(-2)) and (1, g(1)).

(x) = x2 + 1 (a) Find the average rate of change from -1 to 2. (b) Find an equation of the secant line containing (-1, g(-1)) and (2, g(2)).

h(x) = x2 - 2x (a) Find the average rate of change from 2 to 4. (b) Find an equation of the secant line containing (2, h(2)) and (4, h(4))

h(x) = -2x2 + x (a) Find the average rate of change from 0 to 3. (b) Find an equation of the secant line containing (0, h(0)) and (3, h(3)).

g(x) = x3 - 27x (a) Determine whether g is even, odd, or neither. (b) There is a local minimum value of -54 at 3. Determine the local maximum value.

f1x2 = -x3 + 12x (a) Determine whether f is even, odd, or neither. (b) There is a local maximum value of 16 at 2. Determine the local minimum value.

F1x2 = -x4 + 8x2 + 8 (a) Determine whether F is even, odd, or neither. (b) There is a local maximum value of 24 at x = 2. Determine a second local maximum value.

G1x2 = -x4 + 32x2 + 144 (a) Determine whether G is even, odd, or neither. (b) There is a local maximum value of 400 at x = 4. Determine a second local maximum value. (c) Suppose the area under the graph of G between x = 0 and x = 6 that is bounded below by the x-axis is 1612.8 square units. Using the result from part (a), determine the area under the graph of G between x = -6 and x = 0 bounded below by the x-axis.

The average cost per hour in dollars, C, of producing x riding lawn mowers can be modeled by the function C(x) = 0.3x2 + 21x - 251 + 2500 x (a) Use a graphing utility to graph C = C(x). (b) Determine the number of riding lawn mowers to produce in order to minimize average cost. (c) What is the minimum average cost?

The concentration C of a medication in the bloodstream t hours after being administered is modeled by the function C(t) = -0.002t 4 + 0.039t 3 - 0.285t 2 + 0.766t + 0.085 (a) After how many hours will the concentration be highest? (b) A woman nursing a child must wait until the concentration is below 0.5 before she can feed him. After taking the medication, how long must she wait before feeding her child?

The size of the total debt owed by the United States federal government has been growing over the past few years. In fact, according to the Department of the Treasury, the debt per person living in the United States is approximately $45,000 (or over $300,000 per U.S. household)

A strain of E.coli Beu 397-recA441 is placed into a nutrient broth at 30 Celsius and allowed to grow. The data shown in the table are collected. The population is measured in grams and the time in hours. Since population P depends on time t and each input corresponds to exactly one output, we can say that population is a function of time; so P(t) represents the population at time t.

A strain of E.coli Beu 397-recA441 is placed into a nutrient broth at 30 Celsius and allowed to grow. The data shown in the table are collected. The population is measured in grams and the time in hours. Since population P depends on time t and each input corresponds to exactly one output, we can say that population is a function of time; so P(t) represents the population at time t.

For the function f1x2 = x2 , compute each average rate of change: (a) From 1 to 2 (b) From 1 to 1.5 (c) From 1 to 1.1 (d) From 1 to 1.01 (e) From 1 to 1.001 (f) Use a graphing utility to graph each of the secant lines along with f . (g) What do you think is happening to the secant lines? (h) What is happening to the slopes of the secant lines? Is there some number that they are getting closer to? What is that number?

Problems 81 88 require the following discussion of a secant line. The slope of the secant line containing the two points (x, f(x)) and 1x + h, f1x + h22 on the graph of a function y = f1x2 may be given as msec = f1x + h2 - f1x2 1x + h2 - x = f1x + h2 - f1x2 h h 0 In calculus, this expression is called the difference quotient of f. (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find msec for h = 0.5, 0.1, and 0.01 at x = 1. What value does msec approach as h approaches 0? (c) Find the equation for the secant line at x = 1 with h = 0.01. (d) Use a graphing utility to graph f and the secant line found in part (c) on the same viewing window.

Problems 81 88 require the following discussion of a secant line. The slope of the secant line containing the two points (x, f(x)) and 1x + h, f1x + h22 on the graph of a function y = f1x2 may be given as msec = f1x + h2 - f1x2 1x + h2 - x = f1x + h2 - f1x2 h h 0 In calculus, this expression is called the difference quotient of f. (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find msec for h = 0.5, 0.1, and 0.01 at x = 1. What value does msec approach as h approaches 0? (c) Find the equation for the secant line at x = 1 with h = 0.01. (d) Use a graphing utility to graph f and the secant line found in part (c) on the same viewing window.

Problems 81 88 require the following discussion of a secant line. The slope of the secant line containing the two points (x, f(x)) and 1x + h, f1x + h22 on the graph of a function y = f1x2 may be given as msec = f1x + h2 - f1x2 1x + h2 - x = f1x + h2 - f1x2 h h 0 In calculus, this expression is called the difference quotient of f. (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find msec for h = 0.5, 0.1, and 0.01 at x = 1. What value does msec approach as h approaches 0? (c) Find the equation for the secant line at x = 1 with h = 0.01. (d) Use a graphing utility to graph f and the secant line found in part (c) on the same viewing window.

Problems 81 88 require the following discussion of a secant line. The slope of the secant line containing the two points (x, f(x)) and 1x + h, f1x + h22 on the graph of a function y = f1x2 may be given as msec = f1x + h2 - f1x2 1x + h2 - x = f1x + h2 - f1x2 h h 0 In calculus, this expression is called the difference quotient of f. (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find msec for h = 0.5, 0.1, and 0.01 at x = 1. What value does msec approach as h approaches 0? (c) Find the equation for the secant line at x = 1 with h = 0.01. (d) Use a graphing utility to graph f and the secant line found in part (c) on the same viewing window.

Problems 81 88 require the following discussion of a secant line. The slope of the secant line containing the two points (x, f(x)) and 1x + h, f1x + h22 on the graph of a function y = f1x2 may be given as msec = f1x + h2 - f1x2 1x + h2 - x = f1x + h2 - f1x2 h h 0 In calculus, this expression is called the difference quotient of f. (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find msec for h = 0.5, 0.1, and 0.01 at x = 1. What value does msec approach as h approaches 0? (c) Find the equation for the secant line at x = 1 with h = 0.01. (d) Use a graphing utility to graph f and the secant line found in part (c) on the same viewing window.

Problems 81 88 require the following discussion of a secant line. The slope of the secant line containing the two points (x, f(x)) and 1x + h, f1x + h22 on the graph of a function y = f1x2 may be given as msec = f1x + h2 - f1x2 1x + h2 - x = f1x + h2 - f1x2 h h 0 In calculus, this expression is called the difference quotient of f. (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find msec for h = 0.5, 0.1, and 0.01 at x = 1. What value does msec approach as h approaches 0? (c) Find the equation for the secant line at x = 1 with h = 0.01. (d) Use a graphing utility to graph f and the secant line found in part (c) on the same viewing window.

Problems 81 88 require the following discussion of a secant line. The slope of the secant line containing the two points (x, f(x)) and 1x + h, f1x + h22 on the graph of a function y = f1x2 may be given as msec = f1x + h2 - f1x2 1x + h2 - x = f1x + h2 - f1x2 h h 0 In calculus, this expression is called the difference quotient of f. (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find msec for h = 0.5, 0.1, and 0.01 at x = 1. What value does msec approach as h approaches 0? (c) Find the equation for the secant line at x = 1 with h = 0.01. (d) Use a graphing utility to graph f and the secant line found in part (c) on the same viewing window.

Problems 81 88 require the following discussion of a secant line. The slope of the secant line containing the two points (x, f(x)) and 1x + h, f1x + h22 on the graph of a function y = f1x2 may be given as msec = f1x + h2 - f1x2 1x + h2 - x = f1x + h2 - f1x2 h h 0 In calculus, this expression is called the difference quotient of f. (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find msec for h = 0.5, 0.1, and 0.01 at x = 1. What value does msec approach as h approaches 0? (c) Find the equation for the secant line at x = 1 with h = 0.01. (d) Use a graphing utility to graph f and the secant line found in part (c) on the same viewing window.

Draw the graph of a function that has the following properties: domain: all real numbers; range: all real numbers; intercepts: (0, -3) and (3, 0); a local maximum value of -2 is at -1; a local minimum value of -6 is at 2. Compare your graph with those of others. Comment on any differences

Redo Problem 89 with the following additional information: increasing on (- , -1), (2, ); decreasing on (-1, 2). Again compare your graph with others and comment on any differences.

How many x-intercepts can a function defined on an interval have if it is increasing on that interval? Explain.

Suppose that a friend of yours does not understand the idea of increasing and decreasing functions. Provide an explanation, complete with graphs, that clarifies the idea.

Can a function be both even and odd? Explain.

Using a graphing utility, graph y = 5 on the interval (-3, 3). Use MAXIMUM to find the local maximum values on (-3, 3). Comment on the result provided by the calculator.

A function f has a positive average rate of change on the interval 32, 5 4. Is f increasing on 32, 5 4 ? Explain.

Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate of change of y = 24 - x2 on the interval 3 -2, 24. Explain how this can happen.

Open the Secant Line Not Min Point applet. (a) Grab point B and move it just below the x-axis. Verify the slope of the secant line reported in the applet. (b) Move point B closer to point A. What happens to the value of the slope of the secant line? (c) Move point B as close as you can to point A. Describe the secant line as point B approaches point A. Find the equation of the secant line where point B is as close as possible to point A.

Open the Secant Line Min Point applet. In the applet, a localminimum is -7.33 at x = 3(labeled as point A).(a) Grab point B and move it just below the x-axis. Verifythe slope of the secant line reported in the applet.(b) Move point B closer to point A, so that the x-coordinate of point B remains greater than the x-coordinate of point A. What happens to the value of the slope of the secant line? Specifically, what is the sign of the slope of the secant line? (c) Move point B so that the x-coordinate of point B is less than the x-coordinate of point A. What happens to the value of the slope of the secant line? Specifically, what is the sign of the slope of the secant line? (d) As point B moves from the left of point A to the right of point A, note the slope of the secant line. Conjecture the value of the slope of the line tangent to the function at point A.Open the Secant Line Min Point applet. In the applet, a localminimum is -7.33 at x = 3 (labeled as point A).(a) Grab point B and move it just below the x-axis. Verifythe slope of the secant line reported in the applet.