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Popular Functions >

extreme f(x)=x^2*e^x

Solution

extreme points

f (x) = x^{2} \cdot e^{x}

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

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

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

Plug

x = 0

into

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

Minimum (0, 0)

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

Graph

Popular Examples

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extreme f(x,y)=xy+1x+1y

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

Frequently Asked Questions (FAQ)

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