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Exercises 7.3 Practice Problems

1.

Suppose f(x)=x2−2. Compute the average rate of change of f(x) from x=1 to x=5.

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.

3.

Suppose f(x)=x2+2x+3. Compute the average rate of change of f(x) from x=−1 to x=1.

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

5.

Suppose f(x)=x+3x−2. Compute the average rate of change of f(x) from x=0 to x=4.

6.

Suppose f(x)=x3+5x. Compute the average rate of change of f(x) from x=−2 to x=2.

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

8.

Suppose f(x)=x2+16. Compute the average rate of change of f(x) from x=1 to x=10.

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.
116

10.

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

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.

12.

Suppose f(x)=x2−21. Compute the average rate of change of f(x) from x=3 to x=5.

13.

Suppose f(x)=x2−2. Compute the average rate of change of f(x) from x=1 to x=1+h.

Answer.
2+h

14.

Suppose f(x)=3x2+2x. Compute the average rate of change of f(x) from x=2 to x=2+h.

Answer.
3h+10

15.

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

16.

Suppose f(x)=x2+4x+4. Compute the average rate of change of f(x) from x=a to x=a+h.

Answer.
h+2a+4

17.

Suppose f(x)=x2+25. Compute the average rate of change of f(x) from x=5 to x=5+h.

Answer.
10+h

18.

Suppose f(x)=−x2−3x+1. Compute the average rate of change of f(x) from x=a to x=a+h.

Answer.
−2a−h+3

19.

Suppose f(x)=2x2+10x. Compute the average rate of change of f(x) from x=3 to x=3+h.

Answer.
2h+22