What is the extreme f(x)=x^3-3x^2-72x ?

The extreme f(x)=x^3-3x^2-72x is Maximum(-4,176),Minimum(6,-324)

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extreme f(x)=x^3-3x^2-72x

extreme points

f (x) = x^{3} - 3 x^{2} - 72 x

Maximum (- 4, 176), Minimum (6, - 324)

Solution steps

f^{'} (x) = 3 x^{2} - 6 x - 72

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 4

into

x^{3} - 3 x^{2} - 72 x : 176

Maximum (- 4, 176)

Plug

x = 6

into

x^{3} - 3 x^{2} - 72 x : - 324

Minimum (6, - 324)

Maximum (- 4, 176), Minimum (6, - 324)

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

f (x) = 4 x + 12

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

2 - 3 x^{2}

\frac{x + 8}{x ^{2} + x + 1}

What is the extreme f(x)=x^3-3x^2-72x ?
The extreme f(x)=x^3-3x^2-72x is Maximum(-4,176),Minimum(6,-324)