Match List – I with List – II.

Choose the correct answer from the options given below:

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

The correct answer is Option (2) → (A)-(II), (B)-(IV), (C)-(III), (D)-(I)

(A) $y=x^x$

$y'=x^x(1+\log x)=0$

$x=\frac{1}{e}$ stationary point (II)

(B) $y=x^x$

as $y'=x^x(1+\log x)=0$

$⇒x=\frac{1}{e}$

So $\frac{1}{e}$ point of minima

$y_{min}=(\frac{1}{e})^{\frac{1}{e}}=e^{\frac{-1}{e}}$ (IV)

(C) $y=(\frac{1}{x})^x$ so $y=x^{-x}$

$y'=-x^{-x}(1+\log x)=0$

$⇒x=\frac{1}{e}$

so $\frac{1}{e}$ point of maxima

$y_{max}=y(\frac{1}{e})=e^{\frac{1}{e}}$ (III)

(D) $y=\frac{\log x}{x}⇒y'=\frac{1}{x^2}-\frac{\log x}{x^2}=0$

$⇒x=e$ stationary point (I)