What is the extreme f(x)=x^2e^x-3 ?

The extreme f(x)=x^2e^x-3 is Maximum(-2, 4/(e^2)-3),Minimum(0,-3)

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extreme f(x)=x^2e^x-3

extreme points

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

Maximum (- 2, \frac{4}{e ^{2}} - 3), Minimum (0, - 3)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

x^{2} e^{x} - 3 : \frac{4}{e ^{2}} - 3

Maximum (- 2, \frac{4}{e ^{2}} - 3)

Plug

x = 0

into

x^{2} e^{x} - 3 : - 3

Minimum (0, - 3)

Maximum (- 2, \frac{4}{e ^{2}} - 3), Minimum (0, - 3)

What is the extreme f(x)=x^2e^x-3 ?
The extreme f(x)=x^2e^x-3 is Maximum(-2, 4/(e^2)-3),Minimum(0,-3)