What is the extreme x^4-4x^3-18x^2-20x-12 ?

The extreme x^4-4x^3-18x^2-20x-12 is Saddle(-1,-5),Minimum(5,-437)

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extreme x^4-4x^3-18x^2-20x-12

extreme points

x^{4} - 4 x^{3} - 18 x^{2} - 20 x - 12

Saddle (- 1, - 5), Minimum (5, - 437)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x^{2} - 36 x - 20

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 1

into

x^{4} - 4 x^{3} - 18 x^{2} - 20 x - 12 : - 5

Saddle (- 1, - 5)

Plug

x = 5

into

x^{4} - 4 x^{3} - 18 x^{2} - 20 x - 12 : - 437

Minimum (5, - 437)

Saddle (- 1, - 5), Minimum (5, - 437)

- 0.015 x^{2} + 1.24 x - 7.4

f (x, y) = - 3 y^{2} + 18 y - x^{2}

f (x, y) = y ln (2 x + y)

f (x, y) = 5 x^{2} + 5 x - 2 y + 4 y^{2}

f (x, y) = x^{2} + y^{2} - 10 x + 16 y - 6

What is the extreme x^4-4x^3-18x^2-20x-12 ?
The extreme x^4-4x^3-18x^2-20x-12 is Saddle(-1,-5),Minimum(5,-437)