Question

The value of c in Lagrange’ mean value theorem for the function f(x) = x (x – 2) where x∈ [1, 2] is

A. 1

B. \(\frac{1}{2}\)

C. \(\frac{2}{3}\)

D. \(\frac{3}{2}\)

Answer 1

Correct answer is D.

f(x) = x(x – 2)

f(x) = x² – 2x

Since, a polynomial function is always continuous and differentiable.

As f(x) is a polynomial function so it is always continuous on 1, 2 and differentiable on 1, 2.

\(\therefore\) f(x) satisfies both the conditions of Lagrange’s Theorem on 1, 2.

So, a real number has to exist c Є 1, 2, such that