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

The extreme f(x)=-x^3-3x^4 is Maximum(-1/4 , 1/256),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^3-3x^4

extreme points

f (x) = - x^{3} - 3 x^{4}

Maximum (- \frac{1}{4}, \frac{1}{256}), Saddle (0, 0)

Solution steps

f^{'} (x) = - 3 x^{2} - 12 x^{3}

Find intervals:

Increasing

: - \infty < x < - \frac{1}{4},

Decreasing

: - \frac{1}{4} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{1}{4}

into

- x^{3} - 3 x^{4} : \frac{1}{256}

Maximum (- \frac{1}{4}, \frac{1}{256})

Plug

x = 0

into

- x^{3} - 3 x^{4} : 0

Saddle (0, 0)

Maximum (- \frac{1}{4}, \frac{1}{256}), Saddle (0, 0)

What is the extreme f(x)=-x^3-3x^4 ?
The extreme f(x)=-x^3-3x^4 is Maximum(-1/4 , 1/256),Saddle(0,0)