## 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.