2.4 Rates of Change and Tangent Lines Day 1

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Presentation transcript:

2.4 Rates of Change and Tangent Lines Day 1 Calculus AB

Example 1: Find the average rate of change (secant line) of the function over the interval [1,3]

Example 2: See figure on pg. 87 Example 2: See figure on pg. 87. In an experiment, biologists found that after 23 days, there were 150 mosquitos. After 45 days, there were 340 mosquitos. Find the rate at which the population grew.

Vocab/Formulas Slope of Secant Line: average rate of change Slope of Tangent Line: instantaneous rate of change; slope of the curve at point P http://www.math.umn.edu/~garrett/qy/Secant.html http://www.ies.co.jp/math/java/calc/limsec/limsec.html Based on the diagrams and demonstrations, predict a formula for the slope of the tangent.

Example 3: a. ) Find the slope of the tangent and normal lines. b Example 3: a.) Find the slope of the tangent and normal lines. b.) Find the equation of the tangent of the normal line.

Example 4: a. ) Find the slope at x=a. b Example 4: a.) Find the slope at x=a. b.) Determine at what point the slope is –¼

Example 5: Find the speed of a falling rock at t=1.

Assignment Pg.92 1-6 (a’s only), 7-11, 13, 15-17