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Popular Functions >

extreme y=x^2e^x

Solution

extreme

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

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

Plug

x = 0

into

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

Minimum (0, 0)

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

Graph

Popular Examples

extreme f(y)=6x^2+7y^2

extreme f(x)=(t^2)/(1+t^3)

extreme-x^3+6x^2+x-1

extreme f(x,y)=x^3-6xy+y^3+4

extreme-x^3+6x^2+x+1

Frequently Asked Questions (FAQ)

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