Match List-I with List-II
| List-I | List-II | ||
| (Functions) | (Maximum value) | ||
| A | $f(x)=-x^2, x\in (-∞, ∞)$ | I | 8 |
| B | $f(x)=-x^2 +1, x\in (-∞, ∞)$ | II | 7 |
| C | $f(x)= x+1, x \in [0, 6]$ | III | 1 |
| D | $f(x)=x^3, x\in [0, 2]$ | IV | 0 |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
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]
$f(2) = 2^3=8$