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Popular >

extreme x^2e^{-x}

Solution

extreme points

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

inverse of f(x)=(3x+2)/7 inverse

f (x) = \frac{3 x + 2}{7}

intercepts of 2/7 intercepts

\frac{2}{7}

inverse of 2x^2-8x inverse

2 x^{2} - 8 x

inverse of f(x)=-x^3 inverse

f (x) = - x^{3}

intercepts of f(x)=\sqrt[3]{x-2}intercepts

Frequently Asked Questions (FAQ)

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