The Tangent and Velocity Problems

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Presentation transcript:

The Tangent and Velocity Problems AP Calculus August 26, 2015 Mrs. Agnew

Essential Question Essential Vocabulary How do you find the instantaneous rate of change? Essential Vocabulary Tangent Line Problem Velocity Problem Instantaneous Rate of Change

The Tangent Problem What is a tangent line to a graph? What is a secant line to a graph? Review Class Starter Example: Find the equation of the tangent line to the graph of y = x2 at the point P(1,1).

The Tangent Problem How do you find the equation of a tangent line to a curve given only one point? How do you find slope given one point? Slope of tangent line is the limit of the slopes of the secant lines.

The Velocity Problem How do we calculate instantaneous velocity? Example: Suppose that a ball is dropped from the top of a 450 meter tall building. Find the velocity of the ball at 5 seconds. Height, h(t), is given by function h(t) = -4.9t 2 + 450.

The Velocity Problem We cannot find velocity at a single instant in time. We could find average velocity of ball over smaller intervals. The instantaneous velocity is limit of the average velocities over smaller and smaller time intervals. Instantaneous velocity = slope of tangent line.

Guided Practice & Homework Guided Practice (Stewart) Page 99 – 100 #1, 6, 8 Homework (Larson) Page 47 #3, 6, 7