Match List-I with List-II
| List-I | List-II | ||
| (A) | $y=loge^x$ | (I) | $Y''=\frac{1}{e^x}$ |
| (B) | $y=e^{2x}$ | (II) | $y''=\frac{-1}{4x\sqrt{x}}$ |
| (C) | $y=\sqrt{x}$ | (III) | $y''=4e^{2x}$ |
| (D) | $y=e^{-x}$ | (IV) | $y''=0$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(IV), (B)-(III),(C)-(II), (D)-(I)
(A) $y=\log e^x=x\log e=x$
$→y'=1$ and $y''=0$
(B) $y=e^{2x}$
$⇒\frac{dy}{dx}=2e^{2x}⇒\frac{d^2y}{dx^2}=4e^{2x}$
(C) $y=\sqrt{x}$
$⇒\frac{dy}{dx}=\frac{1}{2\sqrt{x}}⇒\frac{d^2y}{dx^2}=\frac{-1}{4x\sqrt{x}}$
(D) $y=e^{-x}$
$⇒\frac{dy}{dx}=-e^{-x}⇒\frac{d^2y}{dx^2}=e^{-x}=\frac{1}{e^x}$