What is the extreme f(x)=(x^4)/4+x^3-14x^2-60x ?

The extreme f(x)=(x^4)/4+x^3-14x^2-60x is Minimum(-6,-36),Maximum(-2,60),Minimum(5,-1475/4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=(x^4)/4+x^3-14x^2-60x

extreme

Minimum (- 6, - 36), Maximum (- 2, 60), Minimum (5, - \frac{1475}{4})

Solution steps

f^{'} (x) = x^{3} + 3 x^{2} - 28 x - 60

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < - 2,

Decreasing

: - 2 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 6

into

\frac{x ^{4}}{4} + x^{3} - 14 x^{2} - 60 x : - 36

Minimum (- 6, - 36)

Plug

x = - 2

into

\frac{x ^{4}}{4} + x^{3} - 14 x^{2} - 60 x : 60

Maximum (- 2, 60)

Plug

x = 5

into

\frac{x ^{4}}{4} + x^{3} - 14 x^{2} - 60 x : - \frac{1475}{4}

Minimum (5, - \frac{1475}{4})

Minimum (- 6, - 36), Maximum (- 2, 60), Minimum (5, - \frac{1475}{4})

What is the extreme f(x)=(x^4)/4+x^3-14x^2-60x ?
The extreme f(x)=(x^4)/4+x^3-14x^2-60x is Minimum(-6,-36),Maximum(-2,60),Minimum(5,-1475/4)