3.1 Section 2.2 Average and Instantaneous Rate of Change

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Presentation transcript:

3.1 Section 2.2 Average and Instantaneous Rate of Change The Derivative of a Function at a Point 3.1

A look at the definition of the first derivative at a point in action Note: Scroll down for the second

Given the graph below, where does the derivative NOT exist?

Let f(x) = ln x a) Find the average rate of change of f between x = 0.99 and x = 1. b) Find the average rate of change of f between x = 1 and x = 1.01. c) Explain why the answer in (a) is to large of an estimate for f ‘ (x) and the answer in (b) is too small of an estimate for f ‘ (x).

Let f(x) = ln x Find the average rate of change of f between x = 0.99 and x = 1 x = 1 and x = 1.01

Let f(x) = ln x a) The average rate of change between x = 0.99 and x = 1 is 1.005 b) The average rate of change between x = 1 and x = 1.01 is 0.995 c) Explain why the answer in (a) is to large of an estimate for f ‘ (x) and the answer in (b) is too small of an estimate for f ‘ (x). (a) is too large and (b) is too small because f(x) is concave down.