What is the extreme f(x)=-3x^3+81x+9 ?

The extreme f(x)=-3x^3+81x+9 is Minimum(-3,-153),Maximum(3,171)

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extreme f(x)=-3x^3+81x+9

extreme points

f (x) = - 3 x^{3} + 81 x + 9

Minimum (- 3, - 153), Maximum (3, 171)

Solution steps

f^{'} (x) = - 9 x^{2} + 81

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

- 3 x^{3} + 81 x + 9 : - 153

Minimum (- 3, - 153)

Plug

x = 3

into

- 3 x^{3} + 81 x + 9 : 171

Maximum (3, 171)

Minimum (- 3, - 153), Maximum (3, 171)

f (x) = x^{\frac{5}{3}} - 6 x^{\frac{2}{3}}

f (r, s) = \frac{2 r}{r ^{4} + 7 s}

f (x) = 1 + \frac{7}{x} - \frac{2}{x ^{2}}

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

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

What is the extreme f(x)=-3x^3+81x+9 ?
The extreme f(x)=-3x^3+81x+9 is Minimum(-3,-153),Maximum(3,171)