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Unformatted text preview: Lecture 11 (Chapter 2, Section 11): Tangents, Velocities and Rates of Change ex. The boiling point B of water (in Fahrenheit degrees) h thousand feet above sea level is given by the function B ( t ) = ¡ 1 : 8 h + 212. What do the intercept and slope of the linear equa tion tell you? By how much does B change starting at sea level if elevation rises by 1000 feet? By how much does B change starting from a mile marker on a trail in the Rockies (5280 feet) if a hiker climbs another 1000 feet? How do we measure rate of change if our function is not linear? Tangent Lines and Slope 6 ? Def. The slope of the secant line through the point P ( a;f ( a )) and a nearby point Q ( x;f ( x )): Def. The tangent line to y = f ( x ) at the point P ( a;f ( a )) is the line through P with slope m = provided that the limit exists. NOTE: We abbreviate to the slope of the curve y = f ( x ) at the point ( a;f ( a ))....
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 Spring '08
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 Calculus, Geometry

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