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
c = 2, -8/3