Applications of derivatives: Tangent and normal lines

The  exercise appears under the Differential calculus Math Mission. This exercise applies derivatives to the idea of tangent and normal lines.

Types of Problems
There are two types of problems in this exercise:


 * 1) Use the graph and answer the application problem: This problem provides a graph and a problem asking for an application of the tangent and/or normal line. The student is expected to find the answer to the question and write it in the space provided.Aodtanl1.png
 * 2) Answer the question directly: This problem presents a problem regarding tangent and normal lines. The student is expected to find the correct answer and write it in the space provided.Aodtanl2.png

Strategies
Knowledge of all the differentiation rules, though particularly product and chain, are encouraged to ensure success on this exercise.
 * 1) The slope of the tangent line is the derivative of the function at the point.
 * 2) The slope of a normal line is the negative reciprocal of the slope of the tangent line at a particular point.

Real-life Applications

 * 1) The derivative attempts to extend the concept of slope to objects that are not lines. It expresses a rate of change.
 * 2) Differential calculus applies to anything that changes or moves over time.