What is the extreme f(x)=x^3-3/2 x^2-6x ?

The extreme f(x)=x^3-3/2 x^2-6x is Maximum(-1, 7/2),Minimum(2,-10)

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extreme f(x)=x^3-3/2 x^2-6x

extreme points

f (x) = x^{3} - \frac{3}{2} x^{2} - 6 x

Maximum (- 1, \frac{7}{2}), Minimum (2, - 10)

Solution steps

f^{'} (x) = 3 x^{2} - 3 x - 6

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

x^{3} - \frac{3}{2} x^{2} - 6 x : \frac{7}{2}

Maximum (- 1, \frac{7}{2})

Plug

x = 2

into

x^{3} - \frac{3}{2} x^{2} - 6 x : - 10

Minimum (2, - 10)

Maximum (- 1, \frac{7}{2}), Minimum (2, - 10)

What is the extreme f(x)=x^3-3/2 x^2-6x ?
The extreme f(x)=x^3-3/2 x^2-6x is Maximum(-1, 7/2),Minimum(2,-10)