Applications of Derivatives: Tangents & Normals Public Class

About the Class

If we look at the graphs of the sine & cosine functions, we observe that at the origin, x=0, the sine curve gives us a 0 as the output while the cosine curve gives us a 1. We also notice that the slope of the tangent at x=pi/2 for the sine curve is 0 which is the value of cosine at the same point x=pi/2. We also, already know that the derivative of the sine function gives us the cosine function.

This observation leads us to the fact that the derivative of a function at a point gives us the slope of the tangent to the curve at that point.

We will use this observation to calculate the slopes of tangents & lines normal/perpendicular to the tangent at this point, called normals to various curves. These can be found out using the basic relation between the tangent & the normal.

We will simply use our differential coefficient along with the equation of a straight line to get along with our first ''Application Of The Derivative''.

Language of instruction:

Keywords: derivatives, pre calculus, tangents, curve, differential coefficient, function