For 1217, sketch the graph of f(x)

For Problems 16, graph the derivative of the given functions

For Problems 16, graph the derivative of the given functions

For Problems 16, graph the derivative of the given functions

For Problems 16, graph the derivative of the given functions

For Problems 16, graph the derivative of the given functions

For Problems 16, graph the derivative of the given functions

The graph of f(x) is given in Figure 2.22. Draw tangent lines to the graph at x = 2, x = 1, x = 0, and x = 2. Estimate f(2), f(1), f(0), and f(2). 4 3 2 1 0 1 2 3 4 1 2 4 x Figure 2.22

The graph of f(x) is given in Figure 2.23. Estimate f(1), f(2), f(3), f(4), and f(5). 1 2 3 4 5 6 1 2 3 4 5 6 f(x) x Figure 2.23

In the graph of f in Figure 2.24, at which of the labeled x-values is (a) f(x) greatest? (b) f(x) least? (c) f(x) greatest? (d) f(x) least? x1 x2 x3 x4 x5 x6 x f(x) Figure 2.24 1

Find approximate values for f(x) at each of the x-values given in the following table. x 0 5 10 15 20 f(x) 100 70 55 46 40 1

Using slopes to left and right of 0, estimate R(0) if R(x) = 100(1.1)x. 1

For Problems 1217, sketch the graph of f(x).

For Problems 1217, sketch the graph of f(x).

For Problems 1217, sketch the graph of f(x).

For Problems 1217, sketch the graph of f(x).

For Problems 1217, sketch the graph of f(x).

For Problems 1217, sketch the graph of f(x).

Match the functions in Problems 1821 with one of the derivatives in Figure 2.25.

Match the functions in Problems 1821 with one of the derivatives in Figure 2.25.

Match the functions in Problems 1821 with one of the derivatives in Figure 2.25.

Match the functions in Problems 1821 with one of the derivatives in Figure 2.25.

A city grew in population throughout the 1980s and into the early 1990s. The population was at its largest in 1995, and then shrank until 2010. Let P = f(t) represent the population of the city t years since 1980. Sketch graphs of f(t) and f(t), labeling the units on the axes. 2

Values of x and g(x) are given in the table. For what value of x does g(x) appear to be closest to 3? x 2.7 3.2 3.7 4.2 4.7 5.2 5.7 6.2 g(x) 3.4 4.4 5.0 5.4 6.0 7.4 9.0 11.0 2

Draw a possible graph of y = f(x) given the following information about its derivative. f(x) > 0 for x < 1 f(x) < 0 for x > 1 f(x) = 0 at x = 1 2

Draw a possible graph of a continuous function y = f(x) that satisfies the following three conditions: f(x) > 0 for 1 < x < 3 f(x) < 0 for x < 1 and x > 3 f(x) = 0 at x = 1 and x = 3 2

A vehiclemoving along a straight road has distance f(t) from its starting point at time t. Which of the graphs in Figure 2.26 could be f(t) for the following scenarios? (Assume the scales on the vertical axes are all the same.) (a) A bus on a popular route, with no traffic (b) A car with no traffic and all green lights (c) A car in heavy traffic conditions t (I) t (II) t (III) Figure 2.26 2

(a) Let f(x) = lnx. Use small intervals to estimate f(1), f(2), f(3), f(4), and f(5). (b) Use your answers to part (a) to guess a formula for the derivative of f(x) = lnx. 2

Suppose f(x) = 1 3x3. Estimate f(2), f(3), and f(4). What do you notice? Can you guess a formula for f(x)? 2

Match each property (a)(d) with one or more of graphs (I)(IV) of functions. (a) f(x) = 1 for all 0 x 4. (b) f(x) > 0 for all 0 x 4 (c) f(2) = 1 (d) f(1) = 2 4 4 x (I) 4 4 x (II) 4 4 x (III) 4 4 x (IV) 3

A child inflates a balloon, admires it for awhile and then lets the air out at a constant rate. If V (t) gives the volume of the balloon at time t, then Figure 2.27 shows V (t) as a function of t. At what time does the child: (a) Begin to inflate the balloon? (b) Finish inflating the balloon? (c) Begin to let the air out? (d) What would the graph of V (t) look like if the child had alternated between pinching and releasing the open end of the balloon, instead of letting the air out at a constant rate?