What is the extreme f(x)=-x^3+9x^2+216x+4766 ?

The extreme f(x)=-x^3+9x^2+216x+4766 is Minimum(-6,4010),Maximum(12,6926)

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extreme f(x)=-x^3+9x^2+216x+4766

extreme points

f (x) = - x^{3} + 9 x^{2} + 216 x + 4766

Minimum (- 6, 4010), Maximum (12, 6926)

Solution steps

f^{'} (x) = - 3 x^{2} + 18 x + 216

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 12,

Decreasing

: 12 < x < \infty

Plug

x = - 6

into

- x^{3} + 9 x^{2} + 216 x + 4766 : 4010

Minimum (- 6, 4010)

Plug

x = 12

into

- x^{3} + 9 x^{2} + 216 x + 4766 : 6926

Maximum (12, 6926)

Minimum (- 6, 4010), Maximum (12, 6926)

f (x) = x + \frac{4}{x}

2 x^{2} - 12 x - 5

x^{\frac{4}{5}} (x^{2} - 7)

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

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

What is the extreme f(x)=-x^3+9x^2+216x+4766 ?
The extreme f(x)=-x^3+9x^2+216x+4766 is Minimum(-6,4010),Maximum(12,6926)