What is the extreme 1/9 x^4-4/9 x^3 ?

The extreme 1/9 x^4-4/9 x^3 is Saddle(0,0),Minimum(3,-3)

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extreme 1/9 x^4-4/9 x^3

extreme points

\frac{1}{9} x^{4} - \frac{4}{9} x^{3}

Saddle (0, 0), Minimum (3, - 3)

Solution steps

f^{'} (x) = \frac{4 x ^{3}}{9} - \frac{4 x ^{2}}{3}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

\frac{1}{9} x^{4} - \frac{4}{9} x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{1}{9} x^{4} - \frac{4}{9} x^{3} : - 3

Minimum (3, - 3)

Saddle (0, 0), Minimum (3, - 3)

x^{2} - x

y = e^{3 x}

x^{2} - 9

\frac{2}{3} x + 8 = y - 3

f (x) = - 2 x^{2} + 1

What is the extreme 1/9 x^4-4/9 x^3 ?
The extreme 1/9 x^4-4/9 x^3 is Saddle(0,0),Minimum(3,-3)