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Math 114: Chapter Two: Limits and DerivativesSection 2.1: The Tangent and Velocity Problemsobjectives
2.Investigation of TangentsConsider the parabolay= (x-3)2and the point (4,1).Find the tangent line toyat the point (4,1).Question:How do we find the slope at (4,1) when we only have that one point?
*Most functions are defined by experimental data.exampleA cardiac monitor is use to measure the heart rate of a patient after surgery. Itcomplies the number of heartbeats aftertminutes. Below is the chart of the collected data.t(minutes)3638404244heartbeats25302661280629483080Q:When we graph this data, what does the slope of the tangent line represent?The monitor estimates this value by calculating the slope of a secant line. Use the data toestimate the patient’s heart rate after 42 minutes using the secant line between the pointswith the given values oft.

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