What is the extreme f(x)=-2x^3+6x^2-9 ?

The extreme f(x)=-2x^3+6x^2-9 is Minimum(0,-9),Maximum(2,-1)

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extreme f(x)=-2x^3+6x^2-9

extreme points

f (x) = - 2 x^{3} + 6 x^{2} - 9

Minimum (0, - 9), Maximum (2, - 1)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

- 2 x^{3} + 6 x^{2} - 9 : - 9

Minimum (0, - 9)

Plug

x = 2

into

- 2 x^{3} + 6 x^{2} - 9 : - 1

Maximum (2, - 1)

Minimum (0, - 9), Maximum (2, - 1)

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

f (x) = \frac{6 x ^{5}}{5} - 15 x^{3} - 81 x + 2

- 0.1 t^{2} 0.8 t + 98.8

f (x, y) = x^{3} + y^{3} - 108 x - 27 y - 6

f (x) = x^{4} + x^{3} - 3 x^{2} - 5 x - 2

What is the extreme f(x)=-2x^3+6x^2-9 ?
The extreme f(x)=-2x^3+6x^2-9 is Minimum(0,-9),Maximum(2,-1)