What is the extreme 6x^4-8x^3-87x^2+90x+24 ?

The extreme 6x^4-8x^3-87x^2+90x+24 is Minimum(-5/2 ,-3083/8),Maximum(1/2 , 373/8),Minimum(3,-219)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme 6x^4-8x^3-87x^2+90x+24

extreme

Minimum (- \frac{5}{2}, - \frac{3083}{8}), Maximum (\frac{1}{2}, \frac{373}{8}), Minimum (3, - 219)

Solution steps

f^{'} (x) = 24 x^{3} - 24 x^{2} - 174 x + 90

Find intervals:

Decreasing

: - \infty < x < - \frac{5}{2},

Increasing

: - \frac{5}{2} < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - \frac{5}{2}

into

6 x^{4} - 8 x^{3} - 87 x^{2} + 90 x + 24 : - \frac{3083}{8}

Minimum (- \frac{5}{2}, - \frac{3083}{8})

Plug

x = \frac{1}{2}

into

6 x^{4} - 8 x^{3} - 87 x^{2} + 90 x + 24 : \frac{373}{8}

Maximum (\frac{1}{2}, \frac{373}{8})

Plug

x = 3

into

6 x^{4} - 8 x^{3} - 87 x^{2} + 90 x + 24 : - 219

Minimum (3, - 219)

Minimum (- \frac{5}{2}, - \frac{3083}{8}), Maximum (\frac{1}{2}, \frac{373}{8}), Minimum (3, - 219)

What is the extreme 6x^4-8x^3-87x^2+90x+24 ?
The extreme 6x^4-8x^3-87x^2+90x+24 is Minimum(-5/2 ,-3083/8),Maximum(1/2 , 373/8),Minimum(3,-219)