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

The extreme f(x)=(x^2-3)e^x is Maximum(-3, 6/(e^3)),Minimum(1,-2e)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=(x^2-3)e^x

extreme points

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

Maximum (- 3, \frac{6}{e ^{3}}), Minimum (1, - 2 e)

Solution steps

f^{'} (x) = e^{x} (x - 1) (x + 3)

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 3

into

(x^{2} - 3) e^{x} : \frac{6}{e ^{3}}

Maximum (- 3, \frac{6}{e ^{3}})

Plug

x = 1

into

(x^{2} - 3) e^{x} : - 2 e

Minimum (1, - 2 e)

Maximum (- 3, \frac{6}{e ^{3}}), Minimum (1, - 2 e)

y = x^{4} - 4 x^{3} + 2

\frac{x + 3}{x ^{2}}

f (x) = x y + \frac{1}{x} + \frac{1}{y}

y = x^{2} + z^{2}

f (x) = \frac{x}{1 + x ^{2}}

What is the extreme f(x)=(x^2-3)e^x ?
The extreme f(x)=(x^2-3)e^x is Maximum(-3, 6/(e^3)),Minimum(1,-2e)