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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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)

y = 2 x^{3} + 3 x^{2} - 12 x

f (x) = y - x

f (x, y) = e^{x - y}

f (x, y) = \frac{1}{2} x^{4} - 3 x y + 3 y^{4}

3 x^{2}

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)