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

The extreme f(x)=x^4-8x^3+3 is Saddle(0,3),Minimum(6,-429)

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

extreme points

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

Saddle (0, 3), Minimum (6, - 429)

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} + 3 : 3

Saddle (0, 3)

Plug

x = 6

into

x^{4} - 8 x^{3} + 3 : - 429

Minimum (6, - 429)

Saddle (0, 3), Minimum (6, - 429)

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

x^{\frac{1}{3}} (x + 4)

f (x, y) = x y (7 + x) (y - 3)

f (x) = \frac{1}{x - 5}

(x - 9)^{2} - 2

What is the extreme f(x)=x^4-8x^3+3 ?
The extreme f(x)=x^4-8x^3+3 is Saddle(0,3),Minimum(6,-429)