What is the extreme x^3-18x^2+81x ?

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

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extreme x^3-18x^2+81x

extreme points

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)

f (x, y) = x^{2} + x y + y^{2} + 8 y

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

\frac{x ^{2} - 9}{x ^{2} - 4}

y = 2 x^{3} - 6 x + 1

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

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