What is the critical f(x)=xe^{1/x} ?

The critical f(x)=xe^{1/x} is x=1

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critical f(x)=xe^{1/x}

critical points

f (x) = x e^{\frac{1}{x}}

x = 1

Solution steps

x e^{\frac{1}{x}}

Find where

f^{'} (x)

is equal to zero or undefined

x = 1, x = 0

Identify critical points not in

f (x)

domain

Domain of

x e^{\frac{1}{x}} : x < 0 or x > 0

x e^{\frac{1}{x}}

is not defined at

x = 0

, therefore:

x = 1

f (x) = 6 x^{2}

f (x) = sin^{2} (2 x)

f (x) = x^{\frac{4}{3}} - 4 x^{\frac{1}{3}}

e^{x^{2}}

f (x, y) = e^{- y^{2} - x^{2}} (y^{2} + x^{2})