Week 4: Derivative of algorithmic, exponential and Trigonometry functions. Curve Sketching. Application of derivatives in Business and Economics.

In geometry, curve sketching are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features. Banks use derivatives to hedge, to reduce the risks involved in the bank's operations. For example, a bank's financial profile might make it vulnerable to losses from changes in interest rates. The bank could purchase interest rate futures to protect itself. Or a pension fund can protect itself against credit default.

  1. Domain. Find the domain of the function and determine the points of discontinuity (if any).
  2. Intercepts. 
  3. Symmetry. 
  4. Asymptotes. 
  5. Intervals of Increase and Decrease. 
  6. Local Maximum and Minimum. 
  7. Concavity/Convexity and Points of Inflection. 
  8. Graph of the Function.