What is the extreme f(x)=x^4+8x^3-2 ?

The extreme f(x)=x^4+8x^3-2 is Minimum(-6,-434),Saddle(0,-2)

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extreme f(x)=x^4+8x^3-2

extreme points

f (x) = x^{4} + 8 x^{3} - 2

Minimum (- 6, - 434), Saddle (0, - 2)

Solution steps

f^{'} (x) = 4 x^{3} + 24 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

x^{4} + 8 x^{3} - 2 : - 434

Minimum (- 6, - 434)

Plug

x = 0

into

x^{4} + 8 x^{3} - 2 : - 2

Saddle (0, - 2)

Minimum (- 6, - 434), Saddle (0, - 2)

f (x) = 2 x^{2} + 3 x y + 4 y^{2} + 5 x - 2 y

- \frac{1}{x}

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

f (x) = 2 x + \frac{8}{x ^{2}}

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

What is the extreme f(x)=x^4+8x^3-2 ?
The extreme f(x)=x^4+8x^3-2 is Minimum(-6,-434),Saddle(0,-2)