The Total Cost (C) and the Total Revenue (R), in dollars, for the production and

The Total Cost (C) and the Total Revenue (R), in dollars, for the production and sale of q hair dryers are given by:
C(q) = 2000 + 5q     and      R(q) = 40q – 0.05q2
Find the interval(s) of quantity q on which the Profit (P) is (i) increasing and (ii) decreasing.

How do relative (or local) minimum points, relative (or local) maximum points, a

How do relative (or local) minimum points, relative (or local) maximum points, and inflection points affect the shape of the graph of a given function?  That is, why might someone use derivative techniques to find these points before sketching the graph of a function (assuming no graphing calculator)?
How does someone determine the intervals over which a function is increasing or decreasing?  What has to be true about the slope of the tangent in each situation (increasing vs. decreasing)?

How do relative (or local) minimum points and relative (or local) maximum points

How do relative (or local) minimum points and relative (or local) maximum points help someone solve an optimization problem? 
What geometric shapes have formulas for calculating area?  What kinds of shapes do not have a geometric formula for calculating area, for which someone would need calculus?
Why are rectangles used in Riemann Sums?  What are some ways that someone can get a pretty good estimate for a given area using Riemann Sums?