What is the extreme 2x^3-6x^2-18x ?

The extreme 2x^3-6x^2-18x is Maximum(-1,10),Minimum(3,-54)

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extreme 2x^3-6x^2-18x

extreme points

2 x^{3} - 6 x^{2} - 18 x

Maximum (- 1, 10), Minimum (3, - 54)

Solution steps

f^{'} (x) = 6 x^{2} - 12 x - 18

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 1

into

2 x^{3} - 6 x^{2} - 18 x : 10

Maximum (- 1, 10)

Plug

x = 3

into

2 x^{3} - 6 x^{2} - 18 x : - 54

Minimum (3, - 54)

Maximum (- 1, 10), Minimum (3, - 54)

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

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} - 7 x - 11 y

f (x, y) = 4 - x^{2} - 4 y^{2}

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

y = x^{3} - 3 x + 2

What is the extreme 2x^3-6x^2-18x ?
The extreme 2x^3-6x^2-18x is Maximum(-1,10),Minimum(3,-54)