This problem illustrates the First Derivative Test. Suppose you compute a derivative of a continuous function g and simplify it as the following: g '(x) = 30x2(10x --1) 10 --x .
(a) Find the critical points of g.
(b) Determine the sign of g ' on each subinterval of the real number line where cp1, cp2, and cp3 refer to the critical points from smallest to largest.