What is the extreme f(x)=x^3-18x^2+81x+45 ?

The extreme f(x)=x^3-18x^2+81x+45 is Maximum(3,153),Minimum(9,45)

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extreme f(x)=x^3-18x^2+81x+45

extreme points

f (x) = x^{3} - 18 x^{2} + 81 x + 45

Maximum (3, 153), Minimum (9, 45)

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 + 45 : 153

Maximum (3, 153)

Plug

x = 9

into

x^{3} - 18 x^{2} + 81 x + 45 : 45

Minimum (9, 45)

Maximum (3, 153), Minimum (9, 45)

2 x^{3} - 6 x^{2} - 18 x

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

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} - 7 x - 11 y

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

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

What is the extreme f(x)=x^3-18x^2+81x+45 ?
The extreme f(x)=x^3-18x^2+81x+45 is Maximum(3,153),Minimum(9,45)