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Popular >

extreme x^2*e^{-x}

Solution

extreme points

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

Minimum (0, 0)

Plug

x = 2

into

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

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

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

Popular Examples

extreme y= 1/(x-2)-3 extreme points

y = \frac{1}{x - 2} - 3

extreme f(x)=x^3+x^2+x extreme points

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

extreme f(x,y)=8y^2-5x^2-10y+2xy extreme points

f (x, y) = 8 y^{2} - 5 x^{2} - 10 y + 2 x y

extreme f(x)= x/(x^2+9x+20)extreme points

f (x) = \frac{x}{x ^{2} + 9 x + 20}

extreme f(x)=2x^3-1 extreme points

f (x) = 2 x^{3} - 1

Frequently Asked Questions (FAQ)

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