Rolle's Theorem and Mean Value Theorem

 $f\left(x\right)=\left(x-3\right)\left(x+1\right)^2,\ \ \ \ \left[-1,3\right]$  

Find the value of c which is guaranteed by Rolle's Theorem.

• -1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

Tags

CCSS.HSA.APR.B.3

• 3

• 0

• 4/5

• Rolle's Theorem doesn't apply

Tags

CCSS.HSA.REI.D.10

• 1/√3

• -1/√3

• ±1/√3

• The MVT doesn't apply

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5

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