What is the extreme f(x)=x^3+12x^2+5 ?

The extreme f(x)=x^3+12x^2+5 is Maximum(-8,261),Minimum(0,5)

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extreme f(x)=x^3+12x^2+5

extreme points

f (x) = x^{3} + 12 x^{2} + 5

Maximum (- 8, 261), Minimum (0, 5)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 8,

Decreasing

: - 8 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 8

into

x^{3} + 12 x^{2} + 5 : 261

Maximum (- 8, 261)

Plug

x = 0

into

x^{3} + 12 x^{2} + 5 : 5

Minimum (0, 5)

Maximum (- 8, 261), Minimum (0, 5)

f (x) = \frac{1}{3 ( 2 x + 6 ) - 12}

f (x) = \frac{3 x ^{2}}{x ^{2} - 4}

f (x) = \frac{3 x + 3}{x + 2}

f (x) = \frac{4}{9} x^{3} - 2 x^{2}

f (x) = \frac{3}{2} x - 3

What is the extreme f(x)=x^3+12x^2+5 ?
The extreme f(x)=x^3+12x^2+5 is Maximum(-8,261),Minimum(0,5)