Consider f(x) = x5 - 15x³. In this question you will find the local minimums and maximums of f (x), and the intervals where f(x) is increasing or decreasing. Use the Problem-Solving Strategy: Using the First Derivative Test (below Theorem 4.9 in the textbook ). a) The derivative of f(x) is: [Select] b) The critical points of f (x) are: [Select] c) Divide (-∞0, ∞o) into subintervals, using the critical points and find the sign of f' in each interval. Using this information we see that: f (x) is increasing on [Select] f(x) is decreasing on [Select] f (x) has a local maximum at [Select] f (x) has a local minimum at [Select]