Mean Value Theorem in Calculus

5-1 The Mean Value Theorem

Guided Notes

Multiple Choice

$$f\left(x\right)=\left(x+3\right)\left(x-1\right)^2,\ \ \ \ \left[-3,1\right]$$   Find the value of c which is guaranteed by Rolle's Theorem.

*Hint: Example 1 

• -1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

Multiple Choice

The value of c guaranteed to exist by the MVT for  $$f\left(x\right)=x^2$$  on the interval [0,3] is:

• 1

• 2

• 3/2

• 1/2

Multiple Choice

$$f\left(x\right)=x^3+2x,\ \ \ \left[-1,1\right]$$   Find the value of c guaranteed by the Mean Value Theorem.

• 1/√3

• -1/√3

• ±1/√3

• The MVT doesn't apply

Multiple Choice

Does the mean value theorem apply to f on [0, 5] ?

• yes

• no

Multiple Choice

• YES

• NO

Multiple Choice

• YES

• NO