What is the extreme f(x)= 2/5 x^5-7x^4+30x^3-27 ?

The extreme f(x)= 2/5 x^5-7x^4+30x^3-27 is Saddle(0,-27),Maximum(5,598),Minimum(9,-2322/5)

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extreme f(x)= 2/5 x^5-7x^4+30x^3-27

extreme points

f (x) = \frac{2}{5} x^{5} - 7 x^{4} + 30 x^{3} - 27

Saddle (0, - 27), Maximum (5, 598), Minimum (9, - \frac{2322}{5})

Solution steps

f^{'} (x) = 2 x^{4} - 28 x^{3} + 90 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 5,

Decreasing

: 5 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = 0

into

\frac{2}{5} x^{5} - 7 x^{4} + 30 x^{3} - 27 : - 27

Saddle (0, - 27)

Plug

x = 5

into

\frac{2}{5} x^{5} - 7 x^{4} + 30 x^{3} - 27 : 598

Maximum (5, 598)

Plug

x = 9

into

\frac{2}{5} x^{5} - 7 x^{4} + 30 x^{3} - 27 : - \frac{2322}{5}

Minimum (9, - \frac{2322}{5})

Saddle (0, - 27), Maximum (5, 598), Minimum (9, - \frac{2322}{5})

f (x, y) = 6 x y - 2 x^{2} y - 3 x y^{2}

f (x, y) = \frac{1}{x y}

16 x y

f (x, y) = x^{2} + y^{2} - 2 x - 6 y + 14

f (x, y) = x^{2} - x^{2} y^{2} + y^{2}

What is the extreme f(x)= 2/5 x^5-7x^4+30x^3-27 ?
The extreme f(x)= 2/5 x^5-7x^4+30x^3-27 is Saddle(0,-27),Maximum(5,598),Minimum(9,-2322/5)