What is the extreme f(x)=x^3-3/2 x^2-18x ?

The extreme f(x)=x^3-3/2 x^2-18x is Maximum(-2,22),Minimum(3,-81/2)

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extreme f(x)=x^3-3/2 x^2-18x

extreme points

f (x) = x^{3} - \frac{3}{2} x^{2} - 18 x

Maximum (- 2, 22), Minimum (3, - \frac{81}{2})

Solution steps

f^{'} (x) = 3 x^{2} - 3 x - 18

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

x^{3} - \frac{3}{2} x^{2} - 18 x : 22

Maximum (- 2, 22)

Plug

x = 3

into

x^{3} - \frac{3}{2} x^{2} - 18 x : - \frac{81}{2}

Minimum (3, - \frac{81}{2})

Maximum (- 2, 22), Minimum (3, - \frac{81}{2})

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

f (x) = \frac{x ^{2}}{( x ^{2} - 1 )}

f (x) = 3 x^{2} - 4 x + 5

f (x) = 2 x - 3 x^{\frac{2}{3}}, - 1 \leq x \leq 3

x (1 - x^{2})^{2}

What is the extreme f(x)=x^3-3/2 x^2-18x ?
The extreme f(x)=x^3-3/2 x^2-18x is Maximum(-2,22),Minimum(3,-81/2)