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

The extreme f(x)=(x^2e^{3x}) is Maximum(-2/3 , 4/(9e^2)),Minimum(0,0)

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

extreme points

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

Maximum (- \frac{2}{3}, \frac{4}{9 e ^{2}}), Minimum (0, 0)

Solution steps

f^{'} (x) = 2 x e^{3 x} + e^{3 x} \cdot 3 x^{2}

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{2}{3}

into

x^{2} e^{3 x} : \frac{4}{9 e ^{2}}

Maximum (- \frac{2}{3}, \frac{4}{9 e ^{2}})

Plug

x = 0

into

x^{2} e^{3 x} : 0

Minimum (0, 0)

Maximum (- \frac{2}{3}, \frac{4}{9 e ^{2}}), Minimum (0, 0)

f (x) = 18500 (0.25 - r^{2})

f (x) = - x^{2} + 8 x - 15, 3 \leq x \leq 5

f (x) = - 2 x^{2} - 2 y^{2} + 20 x + 16 y - 4

f (x) = x^{3} + 3 x^{2} - 45 x

f (x) = \frac{4}{x - 2}, 2 < x \leq 6

What is the extreme f(x)=(x^2e^{3x}) ?
The extreme f(x)=(x^2e^{3x}) is Maximum(-2/3 , 4/(9e^2)),Minimum(0,0)