What is the extreme f(x)=-x^3+x^2+8x+9 ?

The extreme f(x)=-x^3+x^2+8x+9 is Minimum(-4/3 , 67/27),Maximum(2,21)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=-x^3+x^2+8x+9

extreme

Minimum (- \frac{4}{3}, \frac{67}{27}), Maximum (2, 21)

Solution steps

f^{'} (x) = - 3 x^{2} + 2 x + 8

Find intervals:

Decreasing

: - \infty < x < - \frac{4}{3},

Increasing

: - \frac{4}{3} < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - \frac{4}{3}

into

- x^{3} + x^{2} + 8 x + 9 : \frac{67}{27}

Minimum (- \frac{4}{3}, \frac{67}{27})

Plug

x = 2

into

- x^{3} + x^{2} + 8 x + 9 : 21

Maximum (2, 21)

Minimum (- \frac{4}{3}, \frac{67}{27}), Maximum (2, 21)

What is the extreme f(x)=-x^3+x^2+8x+9 ?
The extreme f(x)=-x^3+x^2+8x+9 is Minimum(-4/3 , 67/27),Maximum(2,21)