What is the extreme f(x)=-x^3+9x^2-51 ?

The extreme f(x)=-x^3+9x^2-51 is Minimum(0,-51),Maximum(6,57)

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extreme f(x)=-x^3+9x^2-51

extreme points

f (x) = - x^{3} + 9 x^{2} - 51

Minimum (0, - 51), Maximum (6, 57)

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} - 51 : - 51

Minimum (0, - 51)

Plug

x = 6

into

- x^{3} + 9 x^{2} - 51 : 57

Maximum (6, 57)

Minimum (0, - 51), Maximum (6, 57)

- 3 x

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

f (x) = y + 5 = 2 (x + 1)

3 (\frac{1}{2})^{x}

\frac{3 + 3 x}{x - 2}

What is the extreme f(x)=-x^3+9x^2-51 ?
The extreme f(x)=-x^3+9x^2-51 is Minimum(0,-51),Maximum(6,57)