If #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=3pi/4+2pin# where #n# is any integer

It helps to know some trig derivatives:

$tutorial.math.lamar.edu$

Take the derivative of #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.