What is the inflection tan(x) ?

The inflection tan(x) is (pin,0)

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inflection tan(x)

inflection points

tan (x)

(πn, 0)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = πn, x = \frac{π}{2} + πn

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

tan (x) : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

f (x)

is not defined at

x = \frac{π}{2} + πn

, therefore:

x = πn

Find intervals:

Concave Upward

: πn < x < \frac{π}{2} + πn,

Concave Downward

: \frac{π}{2} + πn < x < π + πn

Plug

x = πn

into

tan (x) : 0

(πn, 0)