What is the extreme f(x)=x^2e^x-6 ?

The extreme f(x)=x^2e^x-6 is Maximum(-2, 4/(e^2)-6),Minimum(0,-6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x^2e^x-6

extreme points

f (x) = x^{2} e^{x} - 6

Maximum (- 2, \frac{4}{e ^{2}} - 6), Minimum (0, - 6)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

x^{2} e^{x} - 6 : \frac{4}{e ^{2}} - 6

Maximum (- 2, \frac{4}{e ^{2}} - 6)

Plug

x = 0

into

x^{2} e^{x} - 6 : - 6

Minimum (0, - 6)

Maximum (- 2, \frac{4}{e ^{2}} - 6), Minimum (0, - 6)

What is the extreme f(x)=x^2e^x-6 ?
The extreme f(x)=x^2e^x-6 is Maximum(-2, 4/(e^2)-6),Minimum(0,-6)