What is the extreme f(x)=x^3-17x^2-24x ?

The extreme f(x)=x^3-17x^2-24x is Maximum(-2/3 , 220/27),Minimum(12,-1008)

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extreme f(x)=x^3-17x^2-24x

extreme points

f (x) = x^{3} - 17 x^{2} - 24 x

Maximum (- \frac{2}{3}, \frac{220}{27}), Minimum (12, - 1008)

Solution steps

f^{'} (x) = 3 x^{2} - 34 x - 24

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < 12,

Increasing

: 12 < x < \infty

Plug

x = - \frac{2}{3}

into

x^{3} - 17 x^{2} - 24 x : \frac{220}{27}

Maximum (- \frac{2}{3}, \frac{220}{27})

Plug

x = 12

into

x^{3} - 17 x^{2} - 24 x : - 1008

Minimum (12, - 1008)

Maximum (- \frac{2}{3}, \frac{220}{27}), Minimum (12, - 1008)

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

300 x^{2} - 1200 x^{3}

f (x) = x^{3} - 3 x^{2} + 4 x - 1

\frac{4 x - 3}{x + 7}

f (x) = \frac{2 x ^{3}}{3} - x^{2} - 12 x

What is the extreme f(x)=x^3-17x^2-24x ?
The extreme f(x)=x^3-17x^2-24x is Maximum(-2/3 , 220/27),Minimum(12,-1008)