NDA 2019 Maths · Mathematics · Application of Derivatives · hard

The function f(x)=x^3 is strictly increasing on mathbb R even though f'(0)=0. 2. The function f(x)=1/x is decreasing on its entire domain mathbb…

Single correct option

Consider the following statements:
1. The function

f(x)=x^3

is strictly increasing on

\mathbb R

even though

f'(0)=0

.
2. The function

f(x)=\frac1x

is decreasing on its entire domain

\mathbb R\setminus\{0\}

.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (A) 1 only

Statement 1:

f'(x)=3x^2\ge0

and vanishes only at the single point

0

, so

f

is strictly increasing; true. Statement 2:

f

decreases on

(-\infty,0)

and on

(0,\infty)

separately, but

f(-1)=-1<f(1)=1

with

-1<1

, so it is not decreasing on the whole domain; false. Only statement 1 is correct.

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