What is the extreme f(x)=-x^3+3x^2+24x-3 ?

The extreme f(x)=-x^3+3x^2+24x-3 is Minimum(-2,-31),Maximum(4,77)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=-x^3+3x^2+24x-3

extreme points

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

Minimum (- 2, - 31), Maximum (4, 77)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 24

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 2

into

- x^{3} + 3 x^{2} + 24 x - 3 : - 31

Minimum (- 2, - 31)

Plug

x = 4

into

- x^{3} + 3 x^{2} + 24 x - 3 : 77

Maximum (4, 77)

Minimum (- 2, - 31), Maximum (4, 77)

f (x) = \frac{4}{y ^{2} - y}

f (x) = 2 x^{2} + 5

3 x^{2} - 2

(2, - 2), (5, 1)

\frac{4 x + 4}{x ^{2} + 3 x + 2}

What is the extreme f(x)=-x^3+3x^2+24x-3 ?
The extreme f(x)=-x^3+3x^2+24x-3 is Minimum(-2,-31),Maximum(4,77)