## 6.5 The Mean Value Theorem for Integrals

1) Consider the function f(x)=3x^2+4x-7

What is the average value of the function on [-2,5]?

2) Consider the function f(x)=4x^3-3x^2+6x-9

What is the average value of the function on [-2,4]?

3) Consider the function f(x)=5x^4-4x^3-3x^2+8x-12

What is the average value of the function on [-3,1]?

4) Consider the function f(x)=3cos(x)-5

What is the average value of the function on [-π,π]?

5) Consider the function f(x)=3e^x+4

What is the exact average value of the function on [0,3]?

Note: Maintain fractions if applicable.

6) Consider the function f(x)=4/x+8. (Supposed to say 4 root x, then outside the root is plus 8).

What is the exact average value of the function on [4,9]?

Note: Maintain fractions if applicable.

7) Consider the function f(x)=3x^2+2x-4

What is the exact value of c in the interval [-2,4] such that f(c)=fave?

Note: Maintain fractions if applicable.

8) Consider the function f(x)=5cos(x)+7

Find the exact value(s) of c in the interval [0,2π] such that f(c)=fave?

Note: For multiple answers, separate using commas and arrange in ascending order. Round

to the nearest hundredth.

9) Consider the function f(x)=4e^x+7

What is the exact value of c in the interval [0,5] such that f(c)=fave?

Note: Maintain fractions if applicable.

10) Consider the function f(x)=3/x+8. (Supposed to say 3 root x, then outside the root is plus 8).

What is the value of c in the interval [4,9] such that f(c)=fave?

Note: Round to the nearest hundredth.