The function would be
f(x) = cosx 2n
<= x <= 2n
+
/4 sin x 2n
+
/4 <= x <= (2n+1)
+
/4 cosx (2n+1)
+
/4 <= x <= (2n+2)
f '(x) = -sinx 2n
<= x <= 2n
+
/4 cosx 2n
+
/4 <= x <= (2n+1)
+
/4 -sinx (2n+1)
+
/4 <= x <= (2n+2)
Here the critical poins are where the function changes its value and the points where f '(x)=0
Now, for n= -1, u'll get the points
now put n=0, and u'll get
Hence, there are 7 points.