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

The extreme f(x)= 1/4 x^4-2x^3+3 is Saddle(0,3),Minimum(6,-105)

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

extreme points

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

Saddle (0, 3), Minimum (6, - 105)

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} + 3 : 3

Saddle (0, 3)

Plug

x = 6

into

\frac{1}{4} x^{4} - 2 x^{3} + 3 : - 105

Minimum (6, - 105)

Saddle (0, 3), Minimum (6, - 105)

f (x) = \frac{( - 8 x ^{3} + 3 x ^{2} )}{4}

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

f (x) = (5 + x)^{5}

f (x, y) = y (e^{x} - 1)

f (x) = \frac{x}{x ^{2} + 9}, - 4 \leq x \leq 5

What is the extreme f(x)= 1/4 x^4-2x^3+3 ?
The extreme f(x)= 1/4 x^4-2x^3+3 is Saddle(0,3),Minimum(6,-105)