Practice Problems

Exercises 7.3 Practice Problems

1.

Suppose $f (x) = x^{2} - 2 .$ Compute the average rate of change of $f (x)$ from $x = 1$ to $x = 5 .$

6

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2.

Suppose $f (x)$ is given in the graph below. Compute the average rate of change of $f (x)$ from $x = - 5$ to $x = 2 .$

Answer.

1

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3.

Suppose $f (x) = x^{2} + 2 x + 3 .$ Compute the average rate of change of $f (x)$ from $x = - 1$ to $x = 1 .$

Answer.

2

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4.

Suppose $g (x)$ is given in the table below. Compute the average rate of change of $g (x)$ from $x = 1$ to $x = 5 .$

Table 7.8.

$x$	$1$	$2$	$3$	$4$	$5$
$g (x)$	$0$	$2$	$4$	$1$	$0$

Answer.

0

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5.

Suppose $f (x) = \frac{x + 3}{x - 2} .$ Compute the average rate of change of $f (x)$ from $x = 0$ to $x = 4 .$

Answer.

\frac{5}{4}

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6.

Suppose $f (x) = x^{3} + 5 x .$ Compute the average rate of change of $f (x)$ from $x = - 2$ to $x = 2 .$

Answer.

9

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7.

Suppose $f (x)$ is given in the table below. Compute the average rate of change of $f (x)$ from $x = 2$ to $x = 5 .$

Table 7.9.

$x$	$2$	$4$	$5$	$7$	$9$
$f (x)$	$1$	$- 2$	$4$	$10$	$0$

Answer.

1

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8.

Suppose $f (x) = x^{2} + 16 .$ Compute the average rate of change of $f (x)$ from $x = 1$ to $x = 10 .$

Answer.

11

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9.

Suppose $g (x)$ is given in the table below. Compute the average rate of change of $g (x)$ from $x = 1$ to $x = 7 .$

Table 7.10.

$x$	$1$	$3$	$5$	$7$	$15$
$g (x)$	$10$	$2$	$14$	$21$	$0$

Answer.

\frac{11}{6}

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10.

Suppose $f (x) = 3 x - 7 .$ Compute the average rate of change of $f (x)$ from $x = - 5$ to $x = - 2 .$

Answer.

3

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11.

Suppose $f (x)$ is given in the graph below. Compute the average rate of change of $f (x)$ from $x = 0$ to $x = 4 .$

Answer.

1

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12.

Suppose $f (x) = x^{2} - 21 .$ Compute the average rate of change of $f (x)$ from $x = 3$ to $x = 5 .$

Answer.

8

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13.

Suppose $f (x) = x^{2} - 2 .$ Compute the average rate of change of $f (x)$ from $x = 1$ to $x = 1 + h .$

Answer.

2 + h

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14.

Suppose $f (x) = 3 x^{2} + 2 x .$ Compute the average rate of change of $f (x)$ from $x = 2$ to $x = 2 + h .$

Answer.

3 h + 10

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15.

Suppose $f (x) = 10 x + 2 .$ Compute the average rate of change of $f (x)$ from $x = a$ to $x = a + h .$

Answer.

10

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16.

Suppose $f (x) = x^{2} + 4 x + 4 .$ Compute the average rate of change of $f (x)$ from $x = a$ to $x = a + h .$

Answer.

h + 2 a + 4

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17.

Suppose $f (x) = x^{2} + 25 .$ Compute the average rate of change of $f (x)$ from $x = 5$ to $x = 5 + h .$

Answer.

10 + h

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18.

Suppose $f (x) = - x^{2} - 3 x + 1 .$ Compute the average rate of change of $f (x)$ from $x = a$ to $x = a + h .$

Answer.

- 2 a - h + 3

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19.

Suppose $f (x) = 2 x^{2} + 10 x .$ Compute the average rate of change of $f (x)$ from $x = 3$ to $x = 3 + h .$

Answer.

2 h + 22