What is the critical f(x)=|x|^x ?

The critical f(x)=|x|^x is x=-1/e ,x= 1/e

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critical f(x)=|x|^x

critical points

f (x) = ∣ x ∣^{x}

x = - \frac{1}{e}, x = \frac{1}{e}

Solution steps

∣ x ∣^{x}

Absolute value functions are piecewise functions

Find the function intervals:

x < 0, x > 0

Evaluate the function behavior for each interval

Find where

f^{'} (x)

is equal to zero or undefined

x = - \frac{1}{e}, x = \frac{1}{e}

f (x, y) = x y - x^{2} - y^{2} - 8 x - 2 y + 4

f (x, y) = x^{2} - 3 y^{2} - 8 x + 9 y + 3 x y

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

f (x) = 3 x^{2} + 4 x + 1

\frac{x + 3}{x ^{2}}