(a) Use a computer algebra system to differentiate the function,

(b) Sketch the graphs of f and f′ on the same set of coordinate axes over the given interval,

(c) Find the critical numbers of f in the open interval, and

(d) Find the interval(s) on which f′ is positive and the interval(s) on which f′ is negative. Compare the behavior of f and the sign of f′.

f(t) = t² sin t, [0, 2π]