What is the extreme f(x)=-2x^3-6x^2+48x+4 ?

The extreme f(x)=-2x^3-6x^2+48x+4 is Minimum(-4,-156),Maximum(2,60)

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extreme f(x)=-2x^3-6x^2+48x+4

extreme points

f (x) = - 2 x^{3} - 6 x^{2} + 48 x + 4

Minimum (- 4, - 156), Maximum (2, 60)

Solution steps

f^{'} (x) = - 6 x^{2} - 12 x + 48

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 4

into

- 2 x^{3} - 6 x^{2} + 48 x + 4 : - 156

Minimum (- 4, - 156)

Plug

x = 2

into

- 2 x^{3} - 6 x^{2} + 48 x + 4 : 60

Maximum (2, 60)

Minimum (- 4, - 156), Maximum (2, 60)

f (x) = sin (2 x) - cos (2 x)

(x - 2)^{2} + 1

f (x, y) = 16 x y - x^{3} - 8 y^{2}

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

f (x) = x^{3} + y^{3} - 9 x y

What is the extreme f(x)=-2x^3-6x^2+48x+4 ?
The extreme f(x)=-2x^3-6x^2+48x+4 is Minimum(-4,-156),Maximum(2,60)