Answer:
7 inflection points
Step-by-step explanation:
The given function [tex]f(x)=sinx+2[/tex] has a midline of y=2 where each point of the function that intersects the line is an inflection point. Inflection points are where the concavity changes, defined by when the second derivative is equal to 0 or undefined.
[tex]f(x)=sin(x)+2[/tex]
[tex]f'(x)=cos(x)[/tex]
[tex]f''(x)=-sin(x)[/tex]
[tex]0=-sin(x)[/tex]
[tex]x=\pi n[/tex] for any integer [tex]n[/tex]
From [tex][-10,10][/tex], there are 7 inflection points, which are[tex]x=-3\pi,-2\pi,-\pi,0,\pi,2\pi,3\pi[/tex]
