Let f(x) = cos2x - 3sen2x, with 0 ≤ x ≤ π. (a) Find all roots of equation f(x) = 0 (b) (i) Find f '(x)     (ii) From the above, find coordinates of points of graph y = f(x) where f ‘(x) = 0  (c) Draw approximately graph y = f(x), showing CLEARLY coordinates of all points where f ‘(x) = 0 and of all points where graph touches coordinate axes.

Find the slope of the tangent to the graph of f(x) = x^2 + 1 at the point (2, 5).  Use the method of finding the slope of the secant between (2, 5) and a neighboring point, and moving the neighboring point closer and closer to (2, 5).  What is important here is the method, not the answer, so show your work very clearly.  A diagram is needed, but you do not need to draw all your secant lines if that becomes difficult.