What is the extreme f(x)=-x^4+8x^3-18x^2 ?

The extreme f(x)=-x^4+8x^3-18x^2 is Maximum(0,0),Saddle(3,-27)

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extreme f(x)=-x^4+8x^3-18x^2

extreme points

f (x) = - x^{4} + 8 x^{3} - 18 x^{2}

Maximum (0, 0), Saddle (3, - 27)

Solution steps

f^{'} (x) = - 4 x^{3} + 24 x^{2} - 36 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

- x^{4} + 8 x^{3} - 18 x^{2} : 0

Maximum (0, 0)

Plug

x = 3

into

- x^{4} + 8 x^{3} - 18 x^{2} : - 27

Saddle (3, - 27)

Maximum (0, 0), Saddle (3, - 27)

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

f (x, y) = - 2 x^{2} - y^{2} + x y + 8 x + 3 y

f (x) = x^{4} - 3 x^{2} + x

f (x) = x^{3} - 12 x^{2} + 45 x + 3

f (x, y) = 1 + 2 x^{2} + 2 y^{2}

What is the extreme f(x)=-x^4+8x^3-18x^2 ?
The extreme f(x)=-x^4+8x^3-18x^2 is Maximum(0,0),Saddle(3,-27)