10 Multiple Choice Calculus

1.

The graph of f ‘(x) is continuous, positive, and has a relative maximum at x = 0. Which of the following statements must be true? (5 points)

	The graph of f is always concave down.
	The graph of f is always increasing.
	The graph of f has a relative maximum at x = 0.
	The graph of f has a relative minimum at x = 0.

2.

Below is the graph of f ‘(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1, and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5. Which of the following statement is false?

(5 points)

	f is concave up from x = -1.5 to x = 1.5.
	f has an inflection point at x = 1.5.
	f has a relative minimum at x = 2.
	All of these are false.

3.

The graph of y = f ‘(x), the derivative of f(x), is shown below. List the intervals where the graph of f is concave down.

(5 points)

	(-4, -2) U (2, 4)
	(-2, 2)
	(-4, 0)
	(0, 4)

4.

Which of the following functions grows the fastest as x grows without bound? (5 points)

	f(x) = ex
	g(x) = ecosx
	h(x) =
	They all grow at the same rate.

5.

Compare the growth rate of the functions f(x) = x³ + 1 and g(x) = x² . (5 points)

	f(x) grows faster than g(x).
	g(x) grows faster than f(x).
	f(x) and g(x) grow at the same rate.
	It cannot be determined.

6.

f is a function that is differentiable for all reals. The value of f ‘(x) is given for several values of x in the table below.

x	-8	-3	0	3	8
f ‘(x)	-4	-2	0	4	5

If f ‘(x) is always increasing, which statement about f(x) must be true? (5 points)

	f(x) passes through the origin.
	f(x) is concave downwards for all x.
	f(x) has a relative minimum at x = 0.
	f(x) has a point of inflection at x = 0.

7.

f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f ‘(x). What is the value of g ‘(0.1)? (5 points)

x	0.1	0.2	0.3	0.4	0.5
f ‘(x)	1	2	3	-4	5

	1
	2
	4
	Cannot be determined

8.

Use the graph of f(t) = 2t + 2 on the interval [-1, 4] to write the function F(x), where . (5 points)

	F(x) = x2 + 3x
	F(x) = x2 + 2x – 12
	F(x) = x2 + 2x – 3
	F(x) = x2 + 4x – 8

9.

The velocity of a particle moving along the x-axis is v(t) = t² + 2t + 1, with t measured in minutes and v(t) measured in feet per minute. To the nearest foot find the total distance travelled by the particle from t = 0 to t = 2 minutes. (5 points)

10.

Find the range of the function . (5 points)

	[-6, 6]
	[0, 6]
	[0, 9π]
	[0, 18π]