What is the extreme f(x)= 2/5 x^5+5x^4+16x^3-15 ?

The extreme f(x)= 2/5 x^5+5x^4+16x^3-15 is Maximum(-6,-507/5),Minimum(-4,-843/5),Saddle(0,-15)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)= 2/5 x^5+5x^4+16x^3-15

extreme points

f (x) = \frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15

Maximum (- 6, - \frac{507}{5}), Minimum (- 4, - \frac{843}{5}), Saddle (0, - 15)

Solution steps

f^{'} (x) = 2 x^{4} + 20 x^{3} + 48 x^{2}

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < - 4,

Increasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

\frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15 : - \frac{507}{5}

Maximum (- 6, - \frac{507}{5})

Plug

x = - 4

into

\frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15 : - \frac{843}{5}

Minimum (- 4, - \frac{843}{5})

Plug

x = 0

into

\frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15 : - 15

Saddle (0, - 15)

Maximum (- 6, - \frac{507}{5}), Minimum (- 4, - \frac{843}{5}), Saddle (0, - 15)

What is the extreme f(x)= 2/5 x^5+5x^4+16x^3-15 ?
The extreme f(x)= 2/5 x^5+5x^4+16x^3-15 is Maximum(-6,-507/5),Minimum(-4,-843/5),Saddle(0,-15)