What is the extreme f(x)=2x^3-3x^2-72x-12 ?

The extreme f(x)=2x^3-3x^2-72x-12 is Maximum(-3,123),Minimum(4,-220)

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extreme f(x)=2x^3-3x^2-72x-12

extreme points

f (x) = 2 x^{3} - 3 x^{2} - 72 x - 12

Maximum (- 3, 123), Minimum (4, - 220)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 3

into

2 x^{3} - 3 x^{2} - 72 x - 12 : 123

Maximum (- 3, 123)

Plug

x = 4

into

2 x^{3} - 3 x^{2} - 72 x - 12 : - 220

Minimum (4, - 220)

Maximum (- 3, 123), Minimum (4, - 220)

15 - 5 x

3 x^{2} - 12 x + 11

f (x) = \frac{5}{2} x - 2

\frac{- 2}{x ^{2}}

What is the extreme f(x)=2x^3-3x^2-72x-12 ?
The extreme f(x)=2x^3-3x^2-72x-12 is Maximum(-3,123),Minimum(4,-220)