What is the extreme f(x)=x^4+2x^3 ?

The extreme f(x)=x^4+2x^3 is Minimum(-3/2 ,-27/16),Saddle(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^4+2x^3

extreme points

f (x) = x^{4} + 2 x^{3}

Minimum (- \frac{3}{2}, - \frac{27}{16}), Saddle (0, 0)

Solution steps

f^{'} (x) = 4 x^{3} + 6 x^{2}

Find intervals:

Decreasing

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

Increasing

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

Increasing

: 0 < x < \infty

Plug

x = - \frac{3}{2}

into

x^{4} + 2 x^{3} : - \frac{27}{16}

Minimum (- \frac{3}{2}, - \frac{27}{16})

Plug

x = 0

into

x^{4} + 2 x^{3} : 0

Saddle (0, 0)

Minimum (- \frac{3}{2}, - \frac{27}{16}), Saddle (0, 0)

What is the extreme f(x)=x^4+2x^3 ?
The extreme f(x)=x^4+2x^3 is Minimum(-3/2 ,-27/16),Saddle(0,0)