What is the inflection tan(2x-5) ?

The inflection tan(2x-5) is ((5-pi)/2+pi/2 n,0)

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inflection tan(2x-5)

inflection points

tan (2 x - 5)

(\frac{5 - π}{2} + \frac{π}{2} n, 0)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = \frac{5 - π}{2} + \frac{π}{2} n, x = \frac{10 - 3 π}{4} + \frac{π}{2} n

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

tan (2 x - 5) : \frac{π}{2} n \leq x < \frac{10 - 3 π}{4} + \frac{π}{2} n or \frac{10 - 3 π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

f (x)

is not defined at

x = \frac{10 - 3 π}{4} + \frac{π}{2} n

, therefore:

x = \frac{5 - π}{2} + \frac{π}{2} n

Find intervals:

Concave Upward

: \frac{π}{2} n \leq x < \frac{10 - 3 π}{4} + \frac{π}{2} n,

Concave Downward

: \frac{10 - 3 π}{4} + \frac{π}{2} n < x < \frac{5 - π}{2} + \frac{π}{2} n,

Concave Upward

: \frac{5 - π}{2} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Plug

x = \frac{5 - π}{2} + \frac{π}{2} n

into

tan (2 x - 5) : 0

(\frac{5 - π}{2} + \frac{π}{2} n, 0)

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

f (x) = x^{2} + 0.45

3 y = 15 x + 60

f (x) = \frac{4 x - 16}{x ^{2} - x - 20}

f (x) = - 3 sin (\frac{1}{2} x - \frac{π}{4}) + 1

What is the inflection tan(2x-5) ?
The inflection tan(2x-5) is ((5-pi)/2+pi/2 n,0)