What is the inflection 3sin(x)+3cos(x) ?

The inflection 3sin(x)+3cos(x) is ((3pi)/4+2pin,0),((7pi)/4+2pin,0)

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inflection 3sin(x)+3cos(x)

inflection points

3 sin (x) + 3 cos (x)

(\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = \frac{3 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

3 sin (x) + 3 cos (x) : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = \frac{3 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Find intervals:

Concave Downward

: 2 πn \leq x < \frac{3 π}{4} + 2 πn,

Concave Upward

: \frac{3 π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn,

Concave Downward

: \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Plug

x = \frac{3 π}{4} + 2 πn

into

3 sin (x) + 3 cos (x) : 0

(\frac{3 π}{4} + 2 πn, 0)

Plug

x = \frac{7 π}{4} + 2 πn

into

3 sin (x) + 3 cos (x) : 0

(\frac{7 π}{4} + 2 πn, 0)

(\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0)

\frac{5}{x ^{2} + 1}

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

f (x) = 5 + \frac{25}{x}

- cos (x)

f (x) = 1 - 2 x^{2}

What is the inflection 3sin(x)+3cos(x) ?
The inflection 3sin(x)+3cos(x) is ((3pi)/4+2pin,0),((7pi)/4+2pin,0)