Calculus I

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Calculus I

• Section 2.1
• Velocity and Tangents

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Homework Section 2.1 The Tangent and Velocity
Problems

• Read Section 2.1
• Problems 1, 3, 4, 5, 8, 9

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D rt

• Draw a Distance/Time graph that represents the
  following A car enters the safety zone between
  Arcata and Eureka doing 70mph. A CHP officer at
  the Indianola exit spots the car and pulls them
  over by the mill. The officer issues a ticket and
  our motorist continues on their way to CR.

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What is a Tangent Line?
Classic definition from Euclid
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What About This?
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What is a Tangent Line?

• Cool Link
• http//www.math.hmc.edu/calculus/tutorials/tangent
  _line/

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Finding the Equation of the Tangent Line

• Lets look at the parabola y x2 and see if we
  can find the equation of the tangent line at
  (1,1). To do this we need to find the slope of
  the line at one point on the parabola. Well use
  the slope of the secant line to help us here.

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Slope of Secant Line
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Slope of the Tangent Line
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The Relation Between the Slope of the Tangent
Line and Velocity

• On a distance/time graph the instantaneous rate
  of change at a point (the slope of the tangent
  line) is the velocity of the object at that
  point.
• If an arrow is shot upward on the moon with a
  velocity of 58 m/s, its height in meters after t
  seconds is given by h 58t 0.83t2. Find the
  velocity after 1 second using mPQ.

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Secants From Data

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