What is the extreme f(x)=-6x^3+9x^2+36x ?

The extreme f(x)=-6x^3+9x^2+36x is Minimum(-1,-21),Maximum(2,60)

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extreme f(x)=-6x^3+9x^2+36x

extreme points

f (x) = - 6 x^{3} + 9 x^{2} + 36 x

Minimum (- 1, - 21), Maximum (2, 60)

Solution steps

f^{'} (x) = - 18 x^{2} + 18 x + 36

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 1

into

- 6 x^{3} + 9 x^{2} + 36 x : - 21

Minimum (- 1, - 21)

Plug

x = 2

into

- 6 x^{3} + 9 x^{2} + 36 x : 60

Maximum (2, 60)

Minimum (- 1, - 21), Maximum (2, 60)

(- 2, - 6), (- 5, 0)

f (x) = 3 x^{4} + 12 x

f (x) = - 3 (4 - x) (4 x + 3)

y + 4 = 3 (x + 1)

12 p

What is the extreme f(x)=-6x^3+9x^2+36x ?
The extreme f(x)=-6x^3+9x^2+36x is Minimum(-1,-21),Maximum(2,60)