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section34_material - Section 3.4 Average Rate of Change...

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MATH 110 BUSINESS CALCULUS CHAPTER 3 INTRODUCTION TO THE DERIVATIVE Section 3.4 Average Rate of Change Recall that symbol (delta) indicates the change. Change in f ( ) ( ) f f b f a = Δ = Change in x x b a = Δ = Difference Quotient: f x Δ Δ What is the meaning? Average Rate of Change of function f over [a, b] Change in ( ) ( ) Change in f f f b f a ARCh x x b a Δ = = = Δ
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Example: Calculate the average rate of change of the given function over the interval [-3,-1]. x -3 -2 -1 0 f(x) -2.4 0 -1.6 0 Solution: Since the interval given is [-3, -1], it implies that in our symbols a = -3 and b = -1. Then, the average rate of change of f over [-3, -1] ( ) ( ) ( 1) ( 3) 1 ( 3) 1.6 ( 2.4) 0.8 0.4 2 2 f b f a f f ARCh b a = = − − − − − = = = Example: If the graph is present, we can also determine the average rate of change of the function from its graph.
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Here is another formula to express the Average Rate of Change: ( ) ( ) f x h f x Average Rate of Change of f h + =
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Example: Calculate the average rate of change of the given function over the interval [a, a+h] for the following h. (Technology is recommended for the cases h = 0.01,
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