What is the extreme 2x^3-3x^2-36x+54 ?

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

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extreme 2x^3-3x^2-36x+54

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, 98)

Plug

x = 3

into

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

Minimum (3, - 27)

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

2 x^{2} - x y + y^{2} + 7 x

f (x, y) = x^{3} + 2 x y^{2} + \frac{y ^{4}}{x}

f (x) = x^{4} - 242 x^{2} - 5

f (x) = 20 x - 10 x - 2

2 x^{3} + 6 x^{2} - 90 x

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