What is the critical f(x)=e^{x^2ln(x)-(x^2)/2} ?

The critical f(x)=e^{x^2ln(x)-(x^2)/2} is x=1

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critical f(x)=e^{x^2ln(x)-(x^2)/2}

critical points

f (x) = e^{x^{2} l n (x) - \frac{x ^{2}}{2}}

x = 1

Solution steps

e^{x^{2} l n (x) - \frac{x ^{2}}{2}}

Find where

f^{'} (x)

is equal to zero or undefined

x = 1, x = 0

Identify critical points not in

f (x)

domain

Domain of

e^{x^{2} l n (x) - \frac{x ^{2}}{2}} : x > 0

e^{x^{2} l n (x) - \frac{x ^{2}}{2}}

is not defined at

x = 0

, therefore:

x = 1

4 x^{3} - 12 x^{2} - 124 x + 132

f (x) = x^{4} - 10 x^{2}

g (t) = t ln (t)

f (x) = - x^{3} + 3 x - 2

f (x) = - x^{3} + 3 x - 1

What is the critical f(x)=e^{x^2ln(x)-(x^2)/2} ?
The critical f(x)=e^{x^2ln(x)-(x^2)/2} is x=1