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Popular >

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}})

Popular Examples

extreme x/(1+x^2)extreme points

\frac{x}{1 + x ^{2}}

extreme f(x)=x^3-5x^2+3x+10 extreme points

f (x) = x^{3} - 5 x^{2} + 3 x + 10

extreme f(x)=e^{-x}extreme points

f (x) = e^{- x}

extreme f(x)=9x^{2/3}+3x-6 extreme points

f (x) = 9 x^{\frac{2}{3}} + 3 x - 6

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

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

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))