What is the extreme f(x)= 1/5 x^5-1/4 x^4-2x^3 ?

The extreme f(x)= 1/5 x^5-1/4 x^4-2x^3 is Maximum(-2, 28/5),Saddle(0,0),Minimum(3,-513/20)

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extreme f(x)= 1/5 x^5-1/4 x^4-2x^3

extreme points

f (x) = \frac{1}{5} x^{5} - \frac{1}{4} x^{4} - 2 x^{3}

Maximum (- 2, \frac{28}{5}), Saddle (0, 0), Minimum (3, - \frac{513}{20})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

\frac{1}{5} x^{5} - \frac{1}{4} x^{4} - 2 x^{3} : \frac{28}{5}

Maximum (- 2, \frac{28}{5})

Plug

x = 0

into

\frac{1}{5} x^{5} - \frac{1}{4} x^{4} - 2 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{1}{5} x^{5} - \frac{1}{4} x^{4} - 2 x^{3} : - \frac{513}{20}

Minimum (3, - \frac{513}{20})

Maximum (- 2, \frac{28}{5}), Saddle (0, 0), Minimum (3, - \frac{513}{20})

What is the extreme f(x)= 1/5 x^5-1/4 x^4-2x^3 ?
The extreme f(x)= 1/5 x^5-1/4 x^4-2x^3 is Maximum(-2, 28/5),Saddle(0,0),Minimum(3,-513/20)