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

The extreme f(x)=2x^4-2x^3 is Saddle(0,0),Minimum(3/4 ,-27/128)

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

extreme points

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

Saddle (0, 0), Minimum (\frac{3}{4}, - \frac{27}{128})

Solution steps

f^{'} (x) = 8 x^{3} - 6 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{3}{4},

Increasing

: \frac{3}{4} < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = \frac{3}{4}

into

2 x^{4} - 2 x^{3} : - \frac{27}{128}

Minimum (\frac{3}{4}, - \frac{27}{128})

Saddle (0, 0), Minimum (\frac{3}{4}, - \frac{27}{128})

\frac{x ^{2} + 1}{1 - x}

f (x) = 6 x^{3} - 9 x^{2} - 216 x + 3

f (x, y) = 338 y^{2} + x^{2} - x^{2} y

f (x) = - 5 x^{3} + 15 x + 2

f (x) = - x^{2} + 6, - 3 \leq x \leq 4

What is the extreme f(x)=2x^4-2x^3 ?
The extreme f(x)=2x^4-2x^3 is Saddle(0,0),Minimum(3/4 ,-27/128)