What is the extreme f(x)=x^3-18x^2+81x ?

The extreme f(x)=x^3-18x^2+81x is Maximum(3,108),Minimum(9,0)

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extreme f(x)=x^3-18x^2+81x

extreme points

f (x) = x^{3} - 18 x^{2} + 81 x

Maximum (3, 108), Minimum (9, 0)

Solution steps

f^{'} (x) = 3 x^{2} - 36 x + 81

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = 3

into

x^{3} - 18 x^{2} + 81 x : 108

Maximum (3, 108)

Plug

x = 9

into

x^{3} - 18 x^{2} + 81 x : 0

Minimum (9, 0)

Maximum (3, 108), Minimum (9, 0)

y = \frac{x ^{2}}{x ^{2} - 1}

f (x) = x^{2} - 4 x y + 5

f (x, y) = 2 x^{4} + y^{4} - 2 x^{2} - 2 y^{2} + 3

f (x) = 9 - 2 x + 4 y - x^{2} - 4 y^{2}

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

What is the extreme f(x)=x^3-18x^2+81x ?
The extreme f(x)=x^3-18x^2+81x is Maximum(3,108),Minimum(9,0)