Verify Lagrange’s mean-value theorem for the following function:
Given:
Since the f(x) is a polynomial function,
It is continuous as well as differentiable in the interval [-1,4].
=10
f' (c)=3c2+2c-6
⇒ 3 c2+2c-6=10
⇒ 3 c2+2c-16=0
⇒ 3 c2-6c+8c-16=0
⇒ 3c(c-2)+8(c-2)=0
⇒ (3c+8)(c-2)=0