What is the extreme y=-x^3+3/2 x^2+18x ?

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

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extreme y=-x^3+3/2 x^2+18x

extreme points

y = - x^{3} + \frac{3}{2} x^{2} + 18 x

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 2

into

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

Minimum (- 2, - 22)

Plug

x = 3

into

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

Maximum (3, \frac{81}{2})

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

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