List of top Mathematics Questions on Absolute maxima and Absolute minima asked in CUET (UG)

A function \[ f(x)=12x^{4/3}-6x^{1/3}, \qquad x\in[-1,1] \] is given. Then, which of the following are TRUE?

(A) $f(x)$ has a critical point at $x=\dfrac{1}{8}$
(B) Absolute maximum value of $f(x)$ is $18$
(C) Absolute maximum value of $f(x)$ is $6$
(D) Absolute minimum value of $f(x)$ is $-\dfrac{9}{4}$

For the function $f(x) = 2x^3 - 9x^2 + 12x - 5, x \in [0, 3]$, match List-I with List-II:

List-I	List-II
(A) Absolute maximum value	(I) 3
(B) Absolute minimum value	(II) 0
(C) Point of maxima	(III) -5
(D) Point of minima	(IV) 4