The given function
f(x) = 2x3 + x2 - 4x - 2 ...(i)
Diff. (i) w.r. to x both sides, we get
f'(x) = 6x2 + 2x - 4
∴ f'(c) = 6c2 + 2c - 4
By Rolle'* Theorems
∴ 6c2 + 2c - 4 = 0
6c2 + 6c - 4c - 4 = 0
6c(c + 1) - 4(c + 1) = 0
(c + 1)(6c - 4) = 0
Hence, verified Rolle'* theorem
