1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider the functions f ( x )= x - sin x and g ( x )= x 4. Statement-1: f ( x ) is increasing for x >0 as well as x <0 and g ( x ) is increasing for x >0 and decreasing for x<0. Statement-2: If an odd function is known to be increasing on the interval x>0 then it is increasing for x <0 also and if an even function is increasing for x >0 then it is decreasing for x <0.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Consider the functions $f ( x )= x -\sin x$ and $g ( x )= x ^4$.
Statement-1 : $f ( x )$ is increasing for $x >0$ as well as $x <0$ and $g ( x )$ is increasing for $x >0$ and decreasing for $x<0$.
Statement-2 : If an odd function is known to be increasing on the interval $x>0$ then it is increasing for $x <0$ also and if an even function is increasing for $x >0$ then it is decreasing for $x <0$.

Application of Derivatives

Solution:

Correct answer is (a) Statement-1 is true, statement- 2 is true and statement-2 is correct explanation for statement- 1 .