What is the extreme f(x)=-4/3 x^3-21/2 x^2-5x+12 ?

The extreme f(x)=-4/3 x^3-21/2 x^2-5x+12 is Minimum(-5,-353/6),Maximum(-1/4 , 1211/96)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=-4/3 x^3-21/2 x^2-5x+12

extreme points

f (x) = - \frac{4}{3} x^{3} - \frac{21}{2} x^{2} - 5 x + 12

Minimum (- 5, - \frac{353}{6}), Maximum (- \frac{1}{4}, \frac{1211}{96})

Solution steps

f^{'} (x) = - 4 x^{2} - 21 x - 5

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

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

Decreasing

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

Plug

x = - 5

into

- \frac{4}{3} x^{3} - \frac{21}{2} x^{2} - 5 x + 12 : - \frac{353}{6}

Minimum (- 5, - \frac{353}{6})

Plug

x = - \frac{1}{4}

into

- \frac{4}{3} x^{3} - \frac{21}{2} x^{2} - 5 x + 12 : \frac{1211}{96}

Maximum (- \frac{1}{4}, \frac{1211}{96})

Minimum (- 5, - \frac{353}{6}), Maximum (- \frac{1}{4}, \frac{1211}{96})

\frac{x + 2}{x ^{2} - 3 x - 10}

y = x^{2} + 10 x + 15

f (x) = 2 - \frac{50}{x ^{2}}

f (x, y) = 4 + 7 x^{2} + 8 y^{2}

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

What is the extreme f(x)=-4/3 x^3-21/2 x^2-5x+12 ?
The extreme f(x)=-4/3 x^3-21/2 x^2-5x+12 is Minimum(-5,-353/6),Maximum(-1/4 , 1211/96)