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

The extreme f(x)=x^3+3x^2-24x is Maximum(-4,80),Minimum(2,-28)

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

extreme points

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

Maximum (- 4, 80), Minimum (2, - 28)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 4

into

x^{3} + 3 x^{2} - 24 x : 80

Maximum (- 4, 80)

Plug

x = 2

into

x^{3} + 3 x^{2} - 24 x : - 28

Minimum (2, - 28)

Maximum (- 4, 80), Minimum (2, - 28)

f (x) = \frac{4}{x} - 1

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

(0, 6), (10, 6)

f (x) = 2 (x + 1)^{3}

\frac{1}{( x + 2 ) ^{3}}

What is the extreme f(x)=x^3+3x^2-24x ?
The extreme f(x)=x^3+3x^2-24x is Maximum(-4,80),Minimum(2,-28)