Consider the function $f(x)=x^3-3x$. Then

Match List-I with List-II

Choose the correct answer from the options given below:

(A)-(II), (B)-(I), (C)-(III), (D)-(IV)

The correct answer is Option (1) → (A)-(II), (B)-(I), (C)-(III), (D)-(IV)

Given

$f(x)=x^3-3x$

$f'(x)=3x^2-3=3(x^2-1)$

Critical points from $f'(x)=0$

$x^2-1=0$

$x=1,-1$

$f''(x)=6x$

$f''(-1)=-6<0$ so $x=-1$ is point of local maxima

$f''(1)=6>0$ so $x=1$ is point of local minima

Local maximum value

$f(-1)=(-1)^3-3(-1)=-1+3=2$

Local minimum value

$f(1)=1-3=-2$

Correct matching: A-II, B-I, C-III, D-IV.