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Popular Functions >

extreme y=x^2e^{-x}

Solution

extreme points

y = x^{2} e^{- x}

Solution

Minimum (0, 0), Maximum (2, \frac{4}{e ^{2}})

Solution steps

f^{'} (x) = e^{- x} x (2 - x)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

x^{2} e^{- x} : 0

Minimum (0, 0)

Plug

x = 2

into

x^{2} e^{- x} : \frac{4}{e ^{2}}

Maximum (2, \frac{4}{e ^{2}})

Minimum (0, 0), Maximum (2, \frac{4}{e ^{2}})

Graph

Popular Examples

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extreme f(x,y)=x^2-x^2y^2+y^2

extreme f(x,y)=3x^2+2y^2

extreme f(x,y)=x-y

Frequently Asked Questions (FAQ)

What is the extreme y=x^2e^{-x} ?
The extreme y=x^2e^{-x} is Minimum(0,0),Maximum(2, 4/(e^2))