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

The extreme f(x)=-x^4+2x^3 is Saddle(0,0),Maximum(3/2 , 27/16)

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

extreme points

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

Saddle (0, 0), Maximum (\frac{3}{2}, \frac{27}{16})

Solution steps

f^{'} (x) = - 4 x^{3} + 6 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{3}{2},

Decreasing

: \frac{3}{2} < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = \frac{3}{2}

into

- x^{4} + 2 x^{3} : \frac{27}{16}

Maximum (\frac{3}{2}, \frac{27}{16})

Saddle (0, 0), Maximum (\frac{3}{2}, \frac{27}{16})

f (x) = - 3 x^{4} + 20 x^{3} - 24 x^{2}

f (x) = x^{2} e^{3 x}

\frac{8 x}{x + 5}

f (x) = \frac{1}{6} x^{2} - 1

\frac{14 x}{x + 14}

What is the extreme f(x)=-x^4+2x^3 ?
The extreme f(x)=-x^4+2x^3 is Saddle(0,0),Maximum(3/2 , 27/16)