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

The extreme f(x)=4x^4-2(4)^2x^3 is Saddle(0,0),Minimum(6,-1728)

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extreme f(x)=4x^4-2(4)^2x^3

extreme points

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

Saddle (0, 0), Minimum (6, - 1728)

Solution steps

f^{'} (x) = 16 x^{3} - 96 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 0

into

4 x^{4} - 2 4^{2} x^{3} : 0

Saddle (0, 0)

Plug

x = 6

into

4 x^{4} - 2 4^{2} x^{3} : - 1728

Minimum (6, - 1728)

Saddle (0, 0), Minimum (6, - 1728)

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

f (x, y) = 400 - 49 x^{2} - 36 y^{2}

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

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

f (x, y) = y^{3} - x^{3} - 3 x y

What is the extreme f(x)=4x^4-2(4)^2x^3 ?
The extreme f(x)=4x^4-2(4)^2x^3 is Saddle(0,0),Minimum(6,-1728)