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If x+y=3e^2t h e d/(dx)(x^y)=0forx= e^2...

If `x+y=3e^2t h e d/(dx)(x^y)=0forx=` `e^2` b. `e^e` c. `e` d. `2e^2`

A

`e`

B

`e^(2)`

C

`e^(e)`

D

`2e^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`y=3e^(2)-x`
`therefore" "x^(y)=x^(3e^(2)-x)`
`" "f(x)=x^(3e^(2)-x)`
`therefore" "log(f(x))=(3e^(2)-x)logx`
`therefore" "(1)/(f(x)).f'(x)=(3e^(2)-x)/(x)-logx`
Now`" "f'(x)=0`
`rArr" "3e^(2)-x=xlogx`
`rArr" "x=e^(2)`
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