Match List – I with List – II.

Choose the correct answer from the options given below:

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

The correct answer is Option (4) → A-III, B-I, C-IV, D-II

$\text{A: } f(x)=4x^3-48x+100$

$f'(x)=12x^2-48=12(x^2-4)=0 \Rightarrow x=\pm2$

$\text{In }[1,3],\ x=2$

$f(1)=56,\ f(2)=36,\ f(3)=64 \Rightarrow \text{maximum}=64$

$\text{B: } f(x)=x^3-18x^2+96x$

$f'(x)=3x^2-36x+96=3(x^2-12x+32)=0 \Rightarrow x=4,8$

$f(0)=0,\ f(4)=160,\ f(8)=128,\ f(9)=162 \Rightarrow \text{minimum}=0$

$\text{C: } f(x)=3x^2-6x$

$f'(x)=6x-6=0 \Rightarrow x=1$

$f(0)=0,\ f(1)=-3,\ f(2)=0 \Rightarrow \text{minimum}=-3$

$\text{D: } f(x)=x^2-8x+17$

$\text{Minimum at } x=\frac{8}{2}=4$

$f(4)=1$

$\text{A-III,\ B-I,\ C-IV,\ D-II}$