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

The extreme f(x)=x^3(1-2x) is Saddle(0,0),Maximum(3/8 , 27/2048)

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extreme f(x)=x^3(1-2x)

extreme

Saddle (0, 0), Maximum (\frac{3}{8}, \frac{27}{2048})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{3}{8},

Decreasing

: \frac{3}{8} < x < \infty

Plug

x = 0

into

x^{3} (1 - 2 x) : 0

Saddle (0, 0)

Plug

x = \frac{3}{8}

into

x^{3} (1 - 2 x) : \frac{27}{2048}

Maximum (\frac{3}{8}, \frac{27}{2048})

Saddle (0, 0), Maximum (\frac{3}{8}, \frac{27}{2048})

What is the extreme f(x)=x^3(1-2x) ?
The extreme f(x)=x^3(1-2x) is Saddle(0,0),Maximum(3/8 , 27/2048)