Derivatives Question

Question

Explain how you estimate the derivative in each of the following ways:

1. As an average rate of change.
2. As an instantaneous rate of change.

Answer 1

An average rate of change is ((x₂) - f(x₁)) / (x₂-x₁)

The instantaneous derivative is the limit as h goes to 0 of (f(x+h)-f(x))/h

You can think of the average rate of change as the "secant" between two points on a curve.

As the two points get closer the secant approaches the tangent, or the "slope" of the curve at a point, the derivative.