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

The extreme f(x)=3x^4-2x^3 is Saddle(0,0),Minimum(1/2 ,-1/16)

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

extreme points

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

Saddle (0, 0), Minimum (\frac{1}{2}, - \frac{1}{16})

Solution steps

f^{'} (x) = 12 x^{3} - 6 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = \frac{1}{2}

into

3 x^{4} - 2 x^{3} : - \frac{1}{16}

Minimum (\frac{1}{2}, - \frac{1}{16})

Saddle (0, 0), Minimum (\frac{1}{2}, - \frac{1}{16})

1 - e^{- 0.5 x}

f (x, y) = 2 x y + \frac{1}{x} + \frac{4}{y}

f (x) = x^{4} - 5 x^{2} = x^{2} (x^{2} - 5)

f (x) = x ln (8 x)

x 7 - x

What is the extreme f(x)=3x^4-2x^3 ?
The extreme f(x)=3x^4-2x^3 is Saddle(0,0),Minimum(1/2 ,-1/16)