What is the extreme f(x)= 1/4 x^4-2x^3+2 ?

The extreme f(x)= 1/4 x^4-2x^3+2 is Saddle(0,2),Minimum(6,-106)

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extreme f(x)= 1/4 x^4-2x^3+2

extreme points

f (x) = \frac{1}{4} x^{4} - 2 x^{3} + 2

Saddle (0, 2), Minimum (6, - 106)

Solution steps

f^{'} (x) = x^{3} - 6 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 0

into

\frac{1}{4} x^{4} - 2 x^{3} + 2 : 2

Saddle (0, 2)

Plug

x = 6

into

\frac{1}{4} x^{4} - 2 x^{3} + 2 : - 106

Minimum (6, - 106)

Saddle (0, 2), Minimum (6, - 106)

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

f (x) = x^{3} + 3 x^{2} + 9, 0 \leq x \leq 10

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

1.5 x^{2} + 45 x + 15000

- x^{3} + 300 x + y^{3} - 48 y + 9

What is the extreme f(x)= 1/4 x^4-2x^3+2 ?
The extreme f(x)= 1/4 x^4-2x^3+2 is Saddle(0,2),Minimum(6,-106)