What is the extreme f(x)=x^4-8x^3+20 ?

The extreme f(x)=x^4-8x^3+20 is Saddle(0,20),Minimum(6,-412)

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extreme f(x)=x^4-8x^3+20

extreme points

f (x) = x^{4} - 8 x^{3} + 20

Saddle (0, 20), Minimum (6, - 412)

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} + 20 : 20

Saddle (0, 20)

Plug

x = 6

into

x^{4} - 8 x^{3} + 20 : - 412

Minimum (6, - 412)

Saddle (0, 20), Minimum (6, - 412)

f (x) = 3 + x + \frac{9}{x}, (0, \infty)

f (x) = x^{\frac{2}{9}} (7 x + 11)

3 x + \frac{75}{x}

x^{2} - y^{2} - 6 x + 6 y + 2

\frac{2 x ^{2} - 8}{- x ^{2} - 2 x + 3}

What is the extreme f(x)=x^4-8x^3+20 ?
The extreme f(x)=x^4-8x^3+20 is Saddle(0,20),Minimum(6,-412)