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

The extreme f(x)=-x^3+9x^2 is Minimum(0,0),Maximum(6,108)

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

extreme points

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

Minimum (0, 0), Maximum (6, 108)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

- x^{3} + 9 x^{2} : 0

Minimum (0, 0)

Plug

x = 6

into

- x^{3} + 9 x^{2} : 108

Maximum (6, 108)

Minimum (0, 0), Maximum (6, 108)

f (x) = x^{2} + x + 2

f (x) = x^{5} = 2 x^{3} = x - 1

\frac{x + 8}{x - 4}

f (x) = 2 \cdot 3^{x - 1} - 4

What is the extreme f(x)=-x^3+9x^2 ?
The extreme f(x)=-x^3+9x^2 is Minimum(0,0),Maximum(6,108)