- 2.2.1: The table shows values of f(x) = x3 near x = 2 (to three decimal pl...
- 2.2.2: By choosing small values for h, estimate the instantaneous rate of ...
- 2.2.3: The income that a company receives from selling an item is called t...
- 2.2.4: (a) Make a table of values rounded to two decimal places for the fu...
- 2.2.5: a) Make a table of values, rounded to two decimal places, for f(x) ...
- 2.2.6: If f(x) = x3 + 4x, estimate f (3) using a table with values of x ne...
- 2.2.7: Graph f(x) = sin x, and use the graph to decide whether the derivat...
- 2.2.8: For the function f(x) = log x, estimate f (1). From the graph of f(...
- 2.2.9: Estimate f (2) for f(x)=3x. Explain your reasoning.
- 2.2.10: The graph of y = f(x) is shown in Figure 2.18. Which is larger in e...
- 2.2.11: Figure 2.19 shows the graph of f. Match the derivatives in the tabl...
- 2.2.12: Label points A, B, C, D, E, and F on the graph of y = f(x) in Figur...
- 2.2.13: Suppose that f(x) is a function with f(100) = 35 and f (100) = 3. E...
- 2.2.14: Show how to represent the following on Figure 2.21. (a) f(4) (b) f(...
- 2.2.15: For each of the following pairs of numbers, use Figure 2.21 to deci...
- 2.2.16: With the function f given by Figure 2.21, arrange the following qua...
- 2.2.17: The function in Figure 2.22 has f(4) = 25 and f (4) = 1.5. Find the...
- 2.2.18: Use Figure 2.23 to fill in the blanks in the following statements a...
- 2.2.19: On a copy of Figure 2.24, mark lengths that represent the quantitie...
- 2.2.20: On a copy of Figure 2.25, mark lengths that represent the quantitie...
- 2.2.21: Consider the function shown in Figure 2.26. (a) Write an expression...
- 2.2.22: (a) If f is even and f (10) = 6, what is f (10)? (b) If f is any ev...
- 2.2.23: If g is an odd function and g (4) = 5, what is g (4)?
- 2.2.24: (a) Estimate f (0) if f(x) = sin x, with x in degrees. (b) In Examp...
- 2.2.25: Find the equation of the tangent line to f(x) = x2 + x at x = 3. Sk...
- 2.2.26: Estimate the instantaneous rate of change of the function f(x) = x ...
- 2.2.27: Estimate the derivative of f(x) = xx at x = 2
- 2.2.28: Estimate the derivative of f(x) = xx at x = 2
- 2.2.29: Let f(x) = ln(cos x). Use your calculator to approximate the instan...
- 2.2.30: On October 17, 2006, in an article called US Population Reaches 300...
- 2.2.31: The population, P(t), of China,3 in billions, can be approximated b...
- 2.2.32: The population, P(t), of China,3 in billions, can be approximated b...
- 2.2.33: Suppose Table 2.3 on page 86 is continued with smaller values of h....
- 2.2.34: (a) Let f(x) = x2. Explain what Table 2.5 tells us about f (1). (b)...
- 2.2.35: Use algebra to evaluate the limits in 3540.
- 2.2.36: Use algebra to evaluate the limits in 3540.
- 2.2.37: Use algebra to evaluate the limits in 3540.
- 2.2.38: Use algebra to evaluate the limits in 3540.
- 2.2.39: Use algebra to evaluate the limits in 3540.
- 2.2.40: Use algebra to evaluate the limits in 3540.
- 2.2.41: Find the derivatives in 4146 algebraicall
- 2.2.42: Find the derivatives in 4146 algebraicall
- 2.2.43: Find the derivatives in 4146 algebraicall
- 2.2.44: Find the derivatives in 4146 algebraicall
- 2.2.45: Find the derivatives in 4146 algebraicall
- 2.2.46: Find the derivatives in 4146 algebraicall
- 2.2.47: Find the derivatives in 4146 algebraicall
- 2.2.48: Find the derivatives in 4146 algebraicall
- 2.2.49: Find the derivatives in 4146 algebraicall
- 2.2.50: Find the derivatives in 4146 algebraicall
- 2.2.51: For the function f(x) = log x we have f (0.5) < 0
- 2.2.52: The derivative of a function f(x) at x = a is the tangent line to t...
- 2.2.53: A continuous function which is always increasing and positive
- 2.2.54: A linear function with derivative 2 at x = 0.
- 2.2.55: You cannot be sure of the exact value of a derivative of a function...
- 2.2.56: If you zoom in (with your calculator) on the graph of y = f(x) in a...
- 2.2.57: If f(x) is concave up, then f (a) < (f(b) f(a))/(b a) for a
- 2.2.58: Assume that f is an odd function and that f (2) = 3, then f (2) = (...
Solutions for Chapter 2.2: THE DERIVATIVE AT A POINT
Full solutions for Calculus: Single Variable | 6th Edition
Addition principle of probability.
P(A or B) = P(A) + P(B) - P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)
Speed of rotation, typically measured in radians or revolutions per unit time
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.
A circular graphical display of categorical data
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers
equation of a parabola
(x - h)2 = 4p(y - k) or (y - k)2 = 4p(x - h)
A statement that compares two quantities using an inequality symbol
The numbers . . ., -3, -2, -1, 0,1,2,...2
Length of an arrow
See Magnitude of an arrow.
Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0
Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.
An arrangement of elements of a set, in which order is important.
Point-slope form (of a line)
y - y1 = m1x - x 12.
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle
A procedure for fitting a quartic function to a set of data.
Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc - ad c2 + d2 i
The function y = sin x.
A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.
A measure of how a data set is spread
Vertical stretch or shrink
See Stretch, Shrink.