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

The extreme f(x)=x^4+4x^3-2 is Minimum(-3,-29),Saddle(0,-2)

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

extreme points

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

Minimum (- 3, - 29), Saddle (0, - 2)

Solution steps

f^{'} (x) = 4 x^{3} + 12 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

x^{4} + 4 x^{3} - 2 : - 29

Minimum (- 3, - 29)

Plug

x = 0

into

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

Saddle (0, - 2)

Minimum (- 3, - 29), Saddle (0, - 2)

f (x, y) = 36 - 9 x^{2} - 4 y^{2}

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

f (x, y) = (x^{2} + y^{2}) \cdot e^{- x - y}

f (x) = 4 - x^{2} - y^{2}

f (x, y) = 4 x y - x^{4} - y^{4}

What is the extreme f(x)=x^4+4x^3-2 ?
The extreme f(x)=x^4+4x^3-2 is Minimum(-3,-29),Saddle(0,-2)