NDA 2019 Maths · Mathematics · Application of Derivatives · easy

For the function f(x)=x^3 on the interval [0,3], the value of c in Lagrange's mean value theorem is

Single correct option

For the function

f(x)=x^3

on the interval

[0,3]

, the value of

c

in Lagrange's mean value theorem is

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Answer: (C) $\sqrt3$

The mean slope is

\frac{f(3)-f(0)}{3-0}=\frac{27}{3}=9

. We need

f'(c)=3c^2=9

, so

c^2=3

and

c=\sqrt3\in(0,3)

. The midpoint

\frac32

is a common wrong guess, valid only for quadratic functions.

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake