If $f (x) = sin x + cos x$ $f(x)=sinx+cosx$ , what are the x-coordinates of the points of inflection of the graph f (x)?

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Answer 1 · 2017-04-14T20:07:12

$x = 3 \frac{π}{4} + 2 π n$ $x=3pi/4+2pin$ where $n$ $n$ is any integer

It helps to know some trig derivatives:

$tutorial.math.lamar.edu$

Take the derivative of $f (x)$ $f(x)$

$f'(x)=cos(x)-sin(x)$

Take the derivative of $f'(x)$

$f"(x)=-sin(x)-cos(x)$

Find when $f"(x)=0$

$0=-sin(x)-cos(x)$

$cos(x)=-sin(x)$

This happens when $x=3pi/4+2pin$ where $n$ is any integer.

If f(x)=sinx+cosxf(x)=sinx+cosxf(x)=sinx+cosx, what are the x-coordinates of the points of inflection of the graph f (x)?