Chapter 3.1 Tangents and the Derivative at a Point

Review Chapter 2 started with finding slope of a curve at a point, and how to measure the rate at which a function changes Finding a Tangent to the Graph of a Function – Calculate slope of secant through a Point P (x 0, f(x 0 )) and a nearby point Q(x 0 +h, f(x 0 +h))

Example Find slope of curve at any point.

Derivative at a Point Started with the difference quotient When adding the limit piece this becomes the definition of the derivative function f at a point x 0 and written f ’(x 0 ) Difference quotient is the average rate of change Derivative is the instantaneous rate of change with respect to x at the point x = x 0

Example: Linear Derivative

Application What is the rate of change of the volume of a ball with respect to the radius when the radius is r = 2?