What is the extreme f(x)=-2/5 x^5+5x^4-16x^3-19 ?

The extreme f(x)=-2/5 x^5+5x^4-16x^3-19 is Saddle(0,-19),Minimum(4,-863/5),Maximum(6,-527/5)

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extreme f(x)=-2/5 x^5+5x^4-16x^3-19

extreme points

f (x) = - \frac{2}{5} x^{5} + 5 x^{4} - 16 x^{3} - 19

Saddle (0, - 19), Minimum (4, - \frac{863}{5}), Maximum (6, - \frac{527}{5})

Solution steps

f^{'} (x) = - 2 x^{4} + 20 x^{3} - 48 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

- \frac{2}{5} x^{5} + 5 x^{4} - 16 x^{3} - 19 : - 19

Saddle (0, - 19)

Plug

x = 4

into

- \frac{2}{5} x^{5} + 5 x^{4} - 16 x^{3} - 19 : - \frac{863}{5}

Minimum (4, - \frac{863}{5})

Plug

x = 6

into

- \frac{2}{5} x^{5} + 5 x^{4} - 16 x^{3} - 19 : - \frac{527}{5}

Maximum (6, - \frac{527}{5})

Saddle (0, - 19), Minimum (4, - \frac{863}{5}), Maximum (6, - \frac{527}{5})

What is the extreme f(x)=-2/5 x^5+5x^4-16x^3-19 ?
The extreme f(x)=-2/5 x^5+5x^4-16x^3-19 is Saddle(0,-19),Minimum(4,-863/5),Maximum(6,-527/5)