Question

Verify Lagrange’s mean-value theorem for the following function:

f(x) = x²+2x+3 on [4, 6]

Answer 1

Given:

Since the f(x) is a polynomial function,

It is continuous as well as differentiable in the interval [4,6].

= 12

⇒ f' (c) = 2c+2

⇒ 2c+2 = 12

⇒ c = 5