What is the extreme y=-4x^3-18x^2+216x-12 ?

The extreme y=-4x^3-18x^2+216x-12 is Minimum(-6,-1092),Maximum(3,366)

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extreme y=-4x^3-18x^2+216x-12

extreme points

y = - 4 x^{3} - 18 x^{2} + 216 x - 12

Minimum (- 6, - 1092), Maximum (3, 366)

Solution steps

f^{'} (x) = - 12 x^{2} - 36 x + 216

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 6

into

- 4 x^{3} - 18 x^{2} + 216 x - 12 : - 1092

Minimum (- 6, - 1092)

Plug

x = 3

into

- 4 x^{3} - 18 x^{2} + 216 x - 12 : 366

Maximum (3, 366)

Minimum (- 6, - 1092), Maximum (3, 366)

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

f (x) = (x^{2} + 1)^{\frac{2}{3}}

f (x) = 2 x^{4} - 7 x^{3} + 4 x^{2} + 2 x + 3

f (x) = 5 t^{2} + 24 t + 136

4 x^{3} - 3 x^{2} - 36 x + 17

What is the extreme y=-4x^3-18x^2+216x-12 ?
The extreme y=-4x^3-18x^2+216x-12 is Minimum(-6,-1092),Maximum(3,366)