What is the extreme f(x)=3x^4+4x^3-36x^2-78 ?

The extreme f(x)=3x^4+4x^3-36x^2-78 is Minimum(-3,-267),Maximum(0,-78),Minimum(2,-142)

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extreme f(x)=3x^4+4x^3-36x^2-78

extreme points

f (x) = 3 x^{4} + 4 x^{3} - 36 x^{2} - 78

Minimum (- 3, - 267), Maximum (0, - 78), Minimum (2, - 142)

Solution steps

f^{'} (x) = 12 x^{3} + 12 x^{2} - 72 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 3

into

3 x^{4} + 4 x^{3} - 36 x^{2} - 78 : - 267

Minimum (- 3, - 267)

Plug

x = 0

into

3 x^{4} + 4 x^{3} - 36 x^{2} - 78 : - 78

Maximum (0, - 78)

Plug

x = 2

into

3 x^{4} + 4 x^{3} - 36 x^{2} - 78 : - 142

Minimum (2, - 142)

Minimum (- 3, - 267), Maximum (0, - 78), Minimum (2, - 142)

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

\frac{D}{D x}

f (x, y) = x^{2} + y^{2} + \frac{2}{x y}

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

f (x, y) = 3 x - 4 y + 7

What is the extreme f(x)=3x^4+4x^3-36x^2-78 ?
The extreme f(x)=3x^4+4x^3-36x^2-78 is Minimum(-3,-267),Maximum(0,-78),Minimum(2,-142)