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in Derivatives by (50.2k points)
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f (x) = xx has a stationary point at

A. x = e
B. x = 1/e
C. x = 1
D. x = e

1 Answer

+1 vote
by (48.8k points)
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Best answer

Given equation is f (x) = xx

Let y= xx………(i)

Taking logarithm on both sides we get

log y=log (xx)

⇒ log y=x log x

Now applying first derivative, we get

Substituting the value of y from equation (i), we get

Now we will find the critical point by equating equation (i) to 0, we get

xx (1+log x)=0

⇒ 1+log x =0 as xx cannot be equal to 0

⇒ log x=-1

But -1=log e-1

⇒ log x=log e-1

Equating the terms we get

x= e-1

x = 1/e

Hence f(x) has a stationary point at  x = 1/e

So the correct option is option B.

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