This problem illustrates the First Derivative Test.

This problem illustrates the First Derivative Test. Suppose you compute a derivative of a continuous function g and simplify it as the following: 9 '(x) = 25x (10x - 1) 10 - X (a) Find the critical points of g. XE (smallest) X E (largest) (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. ---Select--- 0 ---Select-- --Select--- o ---Select-- o cp1 cp2 cp3 (c) Use the signs to classify each critical point as a local maximum, local minimum, or neither. cp1 --Select- cp2 ---Select--- cp3 ---Select