Match List-I with List-II

Choose the correct answer from the options given below :

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

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

(A) $f(x)=-x^2$

$f'(x)=-2x$

∴ Critical point is,

$⇒-2x=0$

$⇒x=0$

But, $f''(x)=-2$

$∴x=0$

(B) $f(x)=-x^2+1$

$f'(x)=-2x$

$f''(x)=-2<0$

∴ Max. Value at $x=0$

$f(0)=1$

(C) $f(x)=x+1$

Max. value at 6. (Triennially)

$f(6)=7$

(D) $f(x)=x^3$,  [0, 2]

$f(2) = 2^3=8$