Profit The profit made by a cinema from selling bags of popcorn can be modeled by (a)

In Exercises 14, evaluate the derivative of the function at the indicated points on the graph. x
x2 x2 4 EX

In Exercises 14, evaluate the derivative of the function at the indicated points on the graph. fx
x 32 x2 fx

In Exercises 14, evaluate the derivative of the function at the indicated points on the graph. fx
x 2 fx 2/3

In Exercises 14, evaluate the derivative of the function at the indicated points on the graph. fx
3xx 1 2
3

In Exercises 58, use the derivative to identify the open intervals on which the function is increasing or decreasing. Verify your result with the graph of the function. fx
x 1  3x 2 1 1

In Exercises 58, use the derivative to identify the open intervals on which the function is increasing or decreasing. Verify your result with the graph of the function. fx
x3 4 fx-3x

In Exercises 58, use the derivative to identify the open intervals on which the function is increasing or decreasing. Verify your result with the graph of the function. fx
x 4  2x2 1

In Exercises 58, use the derivative to identify the open intervals on which the function is increasing or decreasing. Verify your result with the graph of the function. fx
x2 x 1 fx

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. f(x) = 2x - 3

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. f(x) = 5 - 3x

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. g(x) = -(x-1)2

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. g(x) = (x+2)2

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. y
x 2 2x 2  5x

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. y
x y
x 2 2x 2

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. y
x3  6x2

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. y
x  23 y

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. fx
x2  1 y

In Exercises 918, find the critical numbers and the open intervals on which the function is increasing or decreasing. Sketch the graph of the function. fx
4  x2 fx

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. fx
2x 2 8x 10 2 4x 3 fx

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. fx
x fx
2x 2 8x 10 2 4x

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. y
3x 3  3x 2 3 12x2 15x fx

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. y
x y
3x 3  3x 2 3

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. fx
xx 1 x

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. hx
x 3 fx
xx 1 x  1 y

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. fx
x 4  2x3 h

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. fx
1 4x 4  2x2 fx

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. fx
x x2 4 fx

In Exercises 1928, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. fx
x2 x2 4 fx

In Exercises 2934, find the critical numbers and the open intervals on which the function is increasing or decreasing. (Hint:Check for discontinuities.) Sketch the graph of the function. fx
2x 16  x2 f

In Exercises 2934, find the critical numbers and the open intervals on which the function is increasing or decreasing. (Hint:Check for discontinuities.) Sketch the graph of the function. fx
x x 1 fx

In Exercises 2934, find the critical numbers and the open intervals on which the function is increasing or decreasing. (Hint:Check for discontinuities.) Sketch the graph of the function. y
 4  x2 , 2x, x 0 x > 0

In Exercises 2934, find the critical numbers and the open intervals on which the function is increasing or decreasing. (Hint:Check for discontinuities.) Sketch the graph of the function. y
 2x 1, x2  2, x 1 x > 1 y

In Exercises 2934, find the critical numbers and the open intervals on which the function is increasing or decreasing. (Hint:Check for discontinuities.) Sketch the graph of the function. y
 3x 1, 5  x2, x 1 x > 1

In Exercises 2934, find the critical numbers and the open intervals on which the function is increasing or decreasing. (Hint:Check for discontinuities.) Sketch the graph of the function. y
 x3 1, x2 2x, x 0 x > 0 y

Cost The ordering and transportation cost (in hundreds of dollars) for an automobile dealership is modeled by where is the number of automobiles ordered. (a) Find the intervals on which is increasing or decreasing. (b) Use a graphing utility to graph the cost function. (c) Use the trace feature to determine the order sizes for which the cost is $900. Assuming that the revenue function is increasing for which order size would you use? Explain your reasoning.

Chemistry: Molecular Velocity Plots of the relative numbers of (nitrogen) molecules that have a given velocity at each of three temperatures (in degrees Kelvin) are shown in the figure. Identify the differences in the average velocities (indicated by the peaks of the curves) for the three temperatures, and describe the intervals on which the velocity is increasing and decreasing for each of the three temperatures. (Source: Adapted from Zumdahl, Chemistry, Sixth Edition)

Position Function In Exercises 37 and 38, the position function gives the height s (in feet) of a ball, where the time t is measured in seconds. Find the time interval on which the ball is rising and the interval on which it is falling. s
96t  16t 0 t 6

Position Function In Exercises 37 and 38, the position function gives the height s (in feet) of a ball, where the time t is measured in seconds. Find the time interval on which the ball is rising and the interval on which it is falling. s
16t 0 t 4 2 64t,

Law Degrees The number y of law degrees conferred in the United States from 1970 to 2000 can be modeled by where is the time in years, with corresponding to 1970. (Source: U.S. National Center for Education Statistics) (a) Use a graphing utility to graph the model. Then graphically estimate the years during which the model is increasing and the years during which it is decreasing. (b) Use the test for increasing and decreasing functions to verify the result of part (a).

Profit The profit made by a cinema from selling bags of popcorn can be modeled by (a) Find the intervals on which is increasing and decreasing. (b) If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain your reasoning.