What is the extreme f(x)=-2x^3+30x^2-54x+6 ?

The extreme f(x)=-2x^3+30x^2-54x+6 is Minimum(1,-20),Maximum(9,492)

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extreme f(x)=-2x^3+30x^2-54x+6

extreme points

f (x) = - 2 x^{3} + 30 x^{2} - 54 x + 6

Minimum (1, - 20), Maximum (9, 492)

Solution steps

f^{'} (x) = - 6 x^{2} + 60 x - 54

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 9,

Decreasing

: 9 < x < \infty

Plug

x = 1

into

- 2 x^{3} + 30 x^{2} - 54 x + 6 : - 20

Minimum (1, - 20)

Plug

x = 9

into

- 2 x^{3} + 30 x^{2} - 54 x + 6 : 492

Maximum (9, 492)

Minimum (1, - 20), Maximum (9, 492)

f (x) = - 2 x^{3} + 30 x^{2} - 54 x + 8

- 6 x + x^{2}

f (x, y) = 6 x - 8 y + 7 x y

f (x) = - x^{3} + 3 x^{2} - 9

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

What is the extreme f(x)=-2x^3+30x^2-54x+6 ?
The extreme f(x)=-2x^3+30x^2-54x+6 is Minimum(1,-20),Maximum(9,492)