What is the extreme f(x)=x^2e^{13x} ?

The extreme f(x)=x^2e^{13x} is Maximum(-2/13 , 4/(169e^2)),Minimum(0,0)

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extreme f(x)=x^2e^{13x}

extreme points

f (x) = x^{2} e^{13 x}

Maximum (- \frac{2}{13}, \frac{4}{169 e ^{2}}), Minimum (0, 0)

Solution steps

f^{'} (x) = 2 x e^{13 x} + e^{13 x} \cdot 13 x^{2}

Find intervals:

Decreasing

: - \frac{2}{13} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{2}{13}

into

x^{2} e^{13 x} : \frac{4}{169 e ^{2}}

Maximum (- \frac{2}{13}, \frac{4}{169 e ^{2}})

Plug

x = 0

into

x^{2} e^{13 x} : 0

Minimum (0, 0)

Maximum (- \frac{2}{13}, \frac{4}{169 e ^{2}}), Minimum (0, 0)

f (x) = - 2 x (x - 4)

f (x) = - x^{3} + 27 x - 49

f (x) = 2 x - 4 x, x > 0

f (x) = e^{x^{2} - 4}, (- 2, 2)

f (x, y) = \frac{y}{x} + x^{2} y + 6 x

What is the extreme f(x)=x^2e^{13x} ?
The extreme f(x)=x^2e^{13x} is Maximum(-2/13 , 4/(169e^2)),Minimum(0,0)