What is the extreme f(x)=x^3-13x^2-9x ?

The extreme f(x)=x^3-13x^2-9x is Maximum(-1/3 , 41/27),Minimum(9,-405)

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extreme f(x)=x^3-13x^2-9x

extreme points

f (x) = x^{3} - 13 x^{2} - 9 x

Maximum (- \frac{1}{3}, \frac{41}{27}), Minimum (9, - 405)

Solution steps

f^{'} (x) = 3 x^{2} - 26 x - 9

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < 9,

Increasing

: 9 < x < \infty

Plug

x = - \frac{1}{3}

into

x^{3} - 13 x^{2} - 9 x : \frac{41}{27}

Maximum (- \frac{1}{3}, \frac{41}{27})

Plug

x = 9

into

x^{3} - 13 x^{2} - 9 x : - 405

Minimum (9, - 405)

Maximum (- \frac{1}{3}, \frac{41}{27}), Minimum (9, - 405)

3 x^{3} - 9 x + 9 x y^{2}

f (x, y) = \frac{2}{x} + \frac{1}{y} + x y

f (x, y) = \frac{1}{x} + \frac{1}{y} + x y

f (x) = 7 (x - e^{x})

f (x) = 7 x^{2} - 11 x + 5

What is the extreme f(x)=x^3-13x^2-9x ?
The extreme f(x)=x^3-13x^2-9x is Maximum(-1/3 , 41/27),Minimum(9,-405)