Question

Verify Lagranges’ Mean value theorem for the function f(x) = 2x² – 10x + 29 in [2, 9]

Answer 1

f(x) = 2x² – 10x + 29; f'(x) = 4x – 10.
As f is a polynomial, it is continuous in the interval [2, 9] and differentiable in the interval (2, 9).
Therefore two conditions of MVT are satisfied and so there exists c ∈ (2, 9) such that

Hence MVT is verified.