CHAPTER 3 Applications of Differentiation

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Presentation transcript:

CHAPTER 3 Applications of Differentiation 3.1 Extrema on an Interval 3.2 Roll’s Theorem and the Mean Value Theorem 3.3 Increasing and Decreasing Functions and the First Derivative Test 3.4 Concavity and the Second Derivative Test 3.5 Limits at Infinity 3.6 A Summary of Curve Sketching 3.7 Optimization Problems 3.8 Newton’s Method 3.9 Differentials 3.10 Business and Economics Applications

3.1 Extrema on an Interval Goal: Determine the behavior of a function f on an interval I.

ABSOLUTE vs RELATIVE (LOCAL) EXTREMA

HOW TO FIND ‘EXTREMA’??? LOOK FOR CRITICAL NUMBERS

Example 1: Find the EXTREMA by finding the critical points:

Example 2: What is happening f(x) = x3 at x = 0? Is it a critical point?

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