What is the inflection cot(x) ?

The inflection cot(x) is (pi/2+pin,0)

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inflection cot(x)

inflection points

cot (x)

(\frac{π}{2} + πn, 0)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = \frac{π}{2} + πn, x = πn

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

cot (x) : πn < x < π + πn

f (x)

is not defined at

x = πn

, therefore:

x = \frac{π}{2} + πn

Find intervals:

Concave Upward

: πn < x < \frac{π}{2} + πn,

Concave Downward

: \frac{π}{2} + πn < x < π + πn

Plug

x = \frac{π}{2} + πn

into

cot (x) : 0

(\frac{π}{2} + πn, 0)

y = \frac{1}{2}

x^{3} - 9 x^{2} + 15 x

\frac{- 5 x + 25}{9}

2 x^{2} - 7

\frac{5 x + 25}{- x ^{2} + 25}