`f (x) =1 + [cos x ] x, ` in `0 <= x <= x/2` (where [.] denotes greatest integer function)

Let f(x) = sin x (1+cos x) , x in (0,2pi). Find the number of critical points of f(x) . Also identify which of these critical points are points of Maxima // Minima.

Discuss the extremum of f(x) = sin x (1 + cos x), x in (0, pi//2) .

If f(x) = {{:(x cos 1/x, x ne 0),(k ,x =0):} is continous at x=0, then

Let f(x) = |x| cos (1/x) for x ne 0 . Write the down the value of (f) (0) if f is continuous at x = 0

Show that the function f(x) = x cos (1//x), x ne 0 f(0) = 1 is discontinuous at x = 0.