What is the extreme f(x)= 1/2 x^4-2x^3-54x^2+15 ?

The extreme f(x)= 1/2 x^4-2x^3-54x^2+15 is Minimum(-6,-849),Maximum(0,15),Minimum(9,-5073/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)= 1/2 x^4-2x^3-54x^2+15

extreme points

f (x) = \frac{1}{2} x^{4} - 2 x^{3} - 54 x^{2} + 15

Minimum (- 6, - 849), Maximum (0, 15), Minimum (9, - \frac{5073}{2})

Solution steps

f^{'} (x) = 2 x^{3} - 6 x^{2} - 108 x

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Decreasing

: 0 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = - 6

into

\frac{1}{2} x^{4} - 2 x^{3} - 54 x^{2} + 15 : - 849

Minimum (- 6, - 849)

Plug

x = 0

into

\frac{1}{2} x^{4} - 2 x^{3} - 54 x^{2} + 15 : 15

Maximum (0, 15)

Plug

x = 9

into

\frac{1}{2} x^{4} - 2 x^{3} - 54 x^{2} + 15 : - \frac{5073}{2}

Minimum (9, - \frac{5073}{2})

Minimum (- 6, - 849), Maximum (0, 15), Minimum (9, - \frac{5073}{2})

What is the extreme f(x)= 1/2 x^4-2x^3-54x^2+15 ?
The extreme f(x)= 1/2 x^4-2x^3-54x^2+15 is Minimum(-6,-849),Maximum(0,15),Minimum(9,-5073/2)