Question

Verify Rolles theorem for f(x) = x3 2x2 - 8x on [-2,4].​

Answer 1

Step-by-step explanation:

f(x)=x

2

+2x−8

⇒f(x)=(x+4)(x−2)

f

′

(x)=2x+2

We know every polynomial function is continuous and differentiable in R.

In particular f is continuous and differentiable in [−4,2]

Also f(−4)=f(2)=0

Thus there will exist c∈(−4,2) such that f

′

(c)=0

⇒2c+2=0⇒c=−1∈(−4,2)

Hence, Rolle's theorem verified.