OpenStudy (anonymous):

how does one determine MULTIPLE min/max points in a periodic function?

5 years ago
OpenStudy (anonymous):

That would depend on the function, take for example the function sin(x) first: \[\frac{d}{dx}\sin{x}=cos(x)\] now the min max points occur at \[cos(x)=0\] that is at every point on the graph of cos(x) that cos(x)=0 so between the interval \[[-2\pi,2\pi]\] you have cos(x)=0 at \[-\frac{3\pi}{2},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{2}\] then take those x values you got from sin(x)'s derivative namely cos(x), and plug them into sin(x) (the function your trying to find the min max points of) and you will find \[\sin(-\frac{3\pi}{2})=1,\sin(-\frac{\pi}{2})=-1,\sin(\frac{\pi}{2})=1,\sin(\frac{3\pi}{2})=-1\]

5 years ago