What is the extreme f(x)=2x^3+3x^2-36x-54 ?

The extreme f(x)=2x^3+3x^2-36x-54 is Maximum(-3,27),Minimum(2,-98)

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extreme f(x)=2x^3+3x^2-36x-54

extreme points

f (x) = 2 x^{3} + 3 x^{2} - 36 x - 54

Maximum (- 3, 27), Minimum (2, - 98)

Solution steps

f^{'} (x) = 6 x^{2} + 6 x - 36

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 3

into

2 x^{3} + 3 x^{2} - 36 x - 54 : 27

Maximum (- 3, 27)

Plug

x = 2

into

2 x^{3} + 3 x^{2} - 36 x - 54 : - 98

Minimum (2, - 98)

Maximum (- 3, 27), Minimum (2, - 98)

f (x) = \frac{2 e ^{3 x}}{- 3 x - 1}

f (x) = - 3 sin (x) cos (x)

f (x) = \frac{4 x}{x ^{2} + 1}, (- 4, 0)

f (x) = x^{2} + y^{2} - 6 y + 9

f (x) = 8 x^{\frac{3}{4}} - x

What is the extreme f(x)=2x^3+3x^2-36x-54 ?
The extreme f(x)=2x^3+3x^2-36x-54 is Maximum(-3,27),Minimum(2,-98)