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

The critical f(x)= 1/2 x^2e^{-x} is x=0,x=2

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

critical points

f (x) = \frac{1}{2} x^{2} e^{- x}

x = 0, x = 2

Solution steps

\frac{1}{2} x^{2} e^{- x}

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = 2

Identify critical points not in

f (x)

domain

Domain of

\frac{1}{2} x^{2} e^{- x} : - \infty < x < \infty

All critical points are in domain

x = 0, x = 2

y = I n (x + 2)

y = I n (x + 3)

f (x, y) = x^{3} + 3 x y^{2} - 15 x - 12 y

7 + 2 x + 4 y - x^{2} - 4 y^{2}

- x^{2} - 4 x + 9

What is the critical f(x)= 1/2 x^2e^{-x} ?
The critical f(x)= 1/2 x^2e^{-x} is x=0,x=2