Calculus

Application of Derivatives

Medium

core

Consider the function $f(x) = x^4 - 2x^2$ , then which of the following are TRUE?

A. $f(x)$ is increasing on $(-1,0)$

B. $f(x)$ is decreasing on $(0,1)$

C. $f(x)$ is increasing on $(-\infty,-1)$

D. $f(x)$ is decreasing on $(1,\infty)$

Choose the correct answer from the options given below:

A, B,C and D

B and D only

A and B only

C and D only

✅ Correct Option: 3

$f'(x) = 4x(x-1)(x+1)$ .

On $(-\infty,-1)$ the derivative is negative, so $f$ decreases there, making C false.

On $(-1,0)$ it is positive (increasing), on $(0,1)$ negative (decreasing), and on $(1,\infty)$ positive (increasing), so D is false.

Hence only A and B are true.

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Solution