What is the extreme f(x)=-x^3+9x^2-54 ?

The extreme f(x)=-x^3+9x^2-54 is Minimum(0,-54),Maximum(6,54)

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extreme f(x)=-x^3+9x^2-54

extreme

Minimum (0, - 54), Maximum (6, 54)

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} - 54 : - 54

Minimum (0, - 54)

Plug

x = 6

into

- x^{3} + 9 x^{2} - 54 : 54

Maximum (6, 54)

Minimum (0, - 54), Maximum (6, 54)

What is the extreme f(x)=-x^3+9x^2-54 ?
The extreme f(x)=-x^3+9x^2-54 is Minimum(0,-54),Maximum(6,54)