Following is the graph of y = f' (x) , given that f(c) = 0. Analyse the graph and answer the following questions.

(a) How many times the graph of y = f(x) will intersect the x - axis?

(b) Discuss the type of roots of the equation f (x) = 0, ` a le x le b`.

(c) How many points of inflection the graph of ` y = f(x), a le x le b`, has?

(d) Find the points of local maxima/minima of` y = f(x), a lt x b`.

(e) How many roots equation ` f''(x) = 0` has?