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

The extreme f(x)=-x^3+3x^2-9 is Minimum(0,-9),Maximum(2,-5)

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

extreme points

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

Minimum (0, - 9), Maximum (2, - 5)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, - 9)

Plug

x = 2

into

- x^{3} + 3 x^{2} - 9 : - 5

Maximum (2, - 5)

Minimum (0, - 9), Maximum (2, - 5)

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

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

f (x) = 4 x^{3} - 36 x^{2} + 6

f (x) = x^{2} + y^{2} - 14 x + 12 y - 13

f (x) = \frac{( t + 3 ) ^{3}}{( t - 1 ) ^{2}}

What is the extreme f(x)=-x^3+3x^2-9 ?
The extreme f(x)=-x^3+3x^2-9 is Minimum(0,-9),Maximum(2,-5)