What is the extreme f(x)=x^4-8x^3-6 ?

The extreme f(x)=x^4-8x^3-6 is Saddle(0,-6),Minimum(6,-438)

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extreme f(x)=x^4-8x^3-6

extreme points

f (x) = x^{4} - 8 x^{3} - 6

Saddle (0, - 6), Minimum (6, - 438)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 0

into

x^{4} - 8 x^{3} - 6 : - 6

Saddle (0, - 6)

Plug

x = 6

into

x^{4} - 8 x^{3} - 6 : - 438

Minimum (6, - 438)

Saddle (0, - 6), Minimum (6, - 438)

K (r, s) = 3 r - s

f (x) = x (17 - 2 x) (\frac{50}{2} - x)

f (x, y) = 4 x^{2} - x^{2} y + 30 y

f (x, y) = 9 y^{2} - 3 x^{2} - 10 y + 5 x y

f (x) = x^{3} - 5 x^{2} + 3 x + 12, (- 2, 4)

What is the extreme f(x)=x^4-8x^3-6 ?
The extreme f(x)=x^4-8x^3-6 is Saddle(0,-6),Minimum(6,-438)