2.2 The Derivative Function

Main Points
The derivative is the slope of a tangent line to a point in a curve. This is derived from a secant where the point are so close together they are almost one. When a derivative (tangent) is positive (sloping up) the graph is increasing, when 0 (horizontal) the graph is constant and when negative (sloping down) the graph is decreasing. To estimate a derivative numerically we simply use a small difference between two points for the numerator of a slope equation.

Challenges
Considering I have dealt with differentiation before without the explanations on how to get to it by taking the differences of two points over a smaller and smaller range, it makes it a little difficult and frustrating to follow. It feels as though what I learnt before is conflicting with what I'm learnign now even thought they are the same thing.

Reflections
Considering derivatives are instantaeous rates of change for different point over a curve, it would be possible to calculate at which points over a certain car's journey for example that it stopped, (rest stop) sped up (high way) or slowed down (traffic jam.)