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

The extreme f(x)=x^3-2x^4 is Saddle(0,0),Maximum(3/8 , 27/2048)

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

extreme points

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

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} - 2 x^{4} : 0

Saddle (0, 0)

Plug

x = \frac{3}{8}

into

x^{3} - 2 x^{4} : \frac{27}{2048}

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

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

x^{\frac{1}{3}} (x + 4)

f (x, y) = x y (7 + x) (y - 3)

f (x) = \frac{1}{x - 5}

(x - 9)^{2} - 2

f (x) = - \frac{15}{x ^{2} - 19 x + 16}

What is the extreme f(x)=x^3-2x^4 ?
The extreme f(x)=x^3-2x^4 is Saddle(0,0),Maximum(3/8 , 27/2048)