What is the inflection cot(x-pi)-2 ?

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

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inflection cot(x-pi)-2

inflection points

cot (x - π) - 2

(\frac{π}{2} + πn, - 2)

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 - π) - 2 : 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 - π) - 2 : - 2

(\frac{π}{2} + πn, - 2)

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

f (x) = \frac{- 15 + 4 x}{3}

f (x) = \frac{7 + x}{8 - x}

X + 3

\frac{5}{x}

What is the inflection cot(x-pi)-2 ?
The inflection cot(x-pi)-2 is (pi/2+pin,-2)