What is the inflection tan(3x-5) ?

The inflection tan(3x-5) is ((5-pi)/3+pi/3 n,0)

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inflection tan(3x-5)

inflection points

tan (3 x - 5)

(\frac{5 - π}{3} + \frac{π}{3} n, 0)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = \frac{5 - π}{3} + \frac{π}{3} n, x = \frac{10 - 3 π}{6} + \frac{π}{3} n

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

tan (3 x - 5) : \frac{π}{3} n \leq x < \frac{10 - 3 π}{6} + \frac{π}{3} n or \frac{10 - 3 π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

f (x)

is not defined at

x = \frac{10 - 3 π}{6} + \frac{π}{3} n

, therefore:

x = \frac{5 - π}{3} + \frac{π}{3} n

Find intervals:

Concave Upward

: \frac{π}{3} n \leq x < \frac{10 - 3 π}{6} + \frac{π}{3} n,

Concave Downward

: \frac{10 - 3 π}{6} + \frac{π}{3} n < x < \frac{5 - π}{3} + \frac{π}{3} n,

Concave Upward

: \frac{5 - π}{3} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

Plug

x = \frac{5 - π}{3} + \frac{π}{3} n

into

tan (3 x - 5) : 0

(\frac{5 - π}{3} + \frac{π}{3} n, 0)

\frac{2}{x ^{2} - 1}

5 x - 3 y = 8

arctan (tan^{2} (x))

f (x) = \frac{1}{7} x - 9

\frac{1}{x - 3}

What is the inflection tan(3x-5) ?
The inflection tan(3x-5) is ((5-pi)/3+pi/3 n,0)