What is the extreme f(x)=x^2e^{2x} ?

The extreme f(x)=x^2e^{2x} is Maximum(-1, 1/(e^2)),Minimum(0,0)

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extreme f(x)=x^2e^{2x}

extreme points

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

Maximum (- 1, \frac{1}{e ^{2}}), Minimum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 1

into

x^{2} e^{2 x} : \frac{1}{e ^{2}}

Maximum (- 1, \frac{1}{e ^{2}})

Plug

x = 0

into

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

Minimum (0, 0)

Maximum (- 1, \frac{1}{e ^{2}}), Minimum (0, 0)

What is the extreme f(x)=x^2e^{2x} ?
The extreme f(x)=x^2e^{2x} is Maximum(-1, 1/(e^2)),Minimum(0,0)