What is the extreme f(x)=x^3-2x^2-15x ?

The extreme f(x)=x^3-2x^2-15x is Maximum(-5/3 , 400/27),Minimum(3,-36)

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extreme f(x)=x^3-2x^2-15x

extreme points

f (x) = x^{3} - 2 x^{2} - 15 x

Maximum (- \frac{5}{3}, \frac{400}{27}), Minimum (3, - 36)

Solution steps

f^{'} (x) = 3 x^{2} - 4 x - 15

Find intervals:

Increasing

: - \infty < x < - \frac{5}{3},

Decreasing

: - \frac{5}{3} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - \frac{5}{3}

into

x^{3} - 2 x^{2} - 15 x : \frac{400}{27}

Maximum (- \frac{5}{3}, \frac{400}{27})

Plug

x = 3

into

x^{3} - 2 x^{2} - 15 x : - 36

Minimum (3, - 36)

Maximum (- \frac{5}{3}, \frac{400}{27}), Minimum (3, - 36)

y = x^{3} - \frac{3}{2} x^{2}

f (x) = 5 x^{2} - 8 x + 3

f (x) = - x^{3} + 9 x^{2} + 216 x + 4766

f (x) = x + \frac{4}{x}

2 x^{2} - 12 x - 5

What is the extreme f(x)=x^3-2x^2-15x ?
The extreme f(x)=x^3-2x^2-15x is Maximum(-5/3 , 400/27),Minimum(3,-36)