NDA 2023 Maths · Mathematics · Application of Derivatives · easy

The function f(x)=x^2 is increasing on the whole real line. 2. The function f(x)=x^3 is increasing on the whole real line.

Single correct option

Consider the following statements:
1. The function

f(x)=x^2

is increasing on the whole real line.
2. The function

f(x)=x^3

is increasing on the whole real line.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (B) 2 only

For

f(x)=x^2

f'(x)=2x<0

for

x<0

, so it decreases on

(-\infty,0)

and Statement 1 is false. For

f(x)=x^3

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

with equality only at

x=0

, so it is increasing everywhere and Statement 2 is true.

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