Question

Verify Mean Value Theorem, if f (x) = x² – 4x – 3 in the interval [a, b], where a = 1 and b = 4.

Answer 1

f(x) = x² – 4x – 3

Being polynomial function! (x) is continuous is {1,4} and f’ (x) = 2x – 4 and 

hence differentiable (1,4) 

Conditions of Rolle’s theorems are satisfied 

∴ 3 a value c ∈ (1,4) such that

Hence mean value theorem is verified.