Let f(x) = x sin x. (a) Draw the graph f(x) and f'(x) on [, 6]. (b)

Let f(x) = x sin x.
(a) Draw the graph f(x) and f'(x) on [π, 6π].
(b) How many solutions does f(x) = 0 have on [π, 6π]? How many solutions does f'(x) = 0 have on this interval?
(c) What is wrong with the following conjecture? If f and f' are both continuous and differentiable on [a, b], if f(a)= f(b) = 0, and if f(x) = 0 has exactly n - 1 solutions on [a, b].
(d) Determine the maximum value of |f(x) - f'(x)| on [π, 6π].