What is the extreme f(x)= 5/3 x^3-15/2 x^2 ?

The extreme f(x)= 5/3 x^3-15/2 x^2 is Maximum(0,0),Minimum(3,-45/2)

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extreme f(x)= 5/3 x^3-15/2 x^2

extreme points

f (x) = \frac{5}{3} x^{3} - \frac{15}{2} x^{2}

Maximum (0, 0), Minimum (3, - \frac{45}{2})

Solution steps

f^{'} (x) = 5 x^{2} - 15 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

\frac{5}{3} x^{3} - \frac{15}{2} x^{2} : 0

Maximum (0, 0)

Plug

x = 3

into

\frac{5}{3} x^{3} - \frac{15}{2} x^{2} : - \frac{45}{2}

Minimum (3, - \frac{45}{2})

Maximum (0, 0), Minimum (3, - \frac{45}{2})

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

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

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

(- 3, 2), (- 3, - 2)

f (x) = \frac{1}{x ^{2} ( x + 9 )}

What is the extreme f(x)= 5/3 x^3-15/2 x^2 ?
The extreme f(x)= 5/3 x^3-15/2 x^2 is Maximum(0,0),Minimum(3,-45/2)