section34_material

section34_material - MATH110BUSINESSCALCULUS

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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 () ff b f a =Δ = Change in x xb 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 b f a ARCh xx 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 22 fb fa f f ARCh ba −− == = 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 xh 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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This note was uploaded on 10/19/2011 for the course MATH 110 taught by Professor Staff during the Spring '11 term at S.F. State.

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section34_material - MATH110BUSINESSCALCULUS

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