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

The extreme f(x)= 2/5 x^5-5x^4+16x^3+2 is Saddle(0,2),Maximum(4, 778/5),Minimum(6, 442/5)

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

extreme points

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

Saddle (0, 2), Maximum (4, \frac{778}{5}), Minimum (6, \frac{442}{5})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 0

into

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

Saddle (0, 2)

Plug

x = 4

into

\frac{2}{5} x^{5} - 5 x^{4} + 16 x^{3} + 2 : \frac{778}{5}

Maximum (4, \frac{778}{5})

Plug

x = 6

into

\frac{2}{5} x^{5} - 5 x^{4} + 16 x^{3} + 2 : \frac{442}{5}

Minimum (6, \frac{442}{5})

Saddle (0, 2), Maximum (4, \frac{778}{5}), Minimum (6, \frac{442}{5})

What is the extreme f(x)= 2/5 x^5-5x^4+16x^3+2 ?
The extreme f(x)= 2/5 x^5-5x^4+16x^3+2 is Saddle(0,2),Maximum(4, 778/5),Minimum(6, 442/5)