What is the extreme f(x)=x^2e^{10x} ?

The extreme f(x)=x^2e^{10x} is Maximum(-1/5 , 1/(25e^2)),Minimum(0,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x^2e^{10x}

extreme points

f (x) = x^{2} e^{10 x}

Maximum (- \frac{1}{5}, \frac{1}{25 e ^{2}}), Minimum (0, 0)

Solution steps

f^{'} (x) = 2 x e^{10 x} + e^{10 x} \cdot 10 x^{2}

Find intervals:

Increasing

: - \infty < x < - \frac{1}{5},

Decreasing

: - \frac{1}{5} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{1}{5}

into

x^{2} e^{10 x} : \frac{1}{25 e ^{2}}

Maximum (- \frac{1}{5}, \frac{1}{25 e ^{2}})

Plug

x = 0

into

x^{2} e^{10 x} : 0

Minimum (0, 0)

Maximum (- \frac{1}{5}, \frac{1}{25 e ^{2}}), Minimum (0, 0)

What is the extreme f(x)=x^2e^{10x} ?
The extreme f(x)=x^2e^{10x} is Maximum(-1/5 , 1/(25e^2)),Minimum(0,0)