December 3, 2012 Quiz and Rates of Change Do Now: Let’s go over your HW HW2.2d Pg. 117 # 93 - 100.

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Presentation transcript:

December 3, 2012 Quiz and Rates of Change Do Now: Let’s go over your HW HW2.2d Pg. 117 #

What’s on your quiz? Tangent Lines Limit Defn of the Derivative When derivatives exist Graph of derivatives Power Rule, derivative rules, derivatives of sinx, cosx, e x

Rates of Change What is the average rate of change? What is the instantaneous rate of change?

Position A common use for rates of changes are to describe the motion of an object. The position equation s(t) gives the position of an object relative to time. Example: A ball’s position that is dropped from a height of 100 feet is modeled by the equation s(t) = -16t

Velocity The average velocity of an object is given by: (which is also seen as the slope of the secant line) The velocity, or instantaneous velocity, is given by the derivative of the position equation (which is also seen as the slope of the tangent line)

Example A ball’s position that is dropped from a height of 100 feet is modeled by the equation s(t) = -16t )What is the average velocity over the time interval [1, 2]? 2)What equation represents the velocity at any time t? 3)What is the velocity of the ball at t = 2?

Practice At time t = 0, a diver jumps from a platform diving board that is 32 feet above water. The position of the diver is given by s(t) = -16t t + 32 where s is measured in feet and t is measured in seconds. 1)When does the diver hit the water? 2)What is the diver’s velocity at impact?