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,-426)

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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, - 426)

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 : - 426

Minimum (6, - 426)

Saddle (0, 6), Minimum (6, - 426)

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

f (x) = - \frac{6 x}{3 x ^{2} + 8}

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

Y (A, B) = A B + A B + A B

x^{2} - x

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,-426)