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calc notes lecture 9

calc notes lecture 9 - after blood leaves the heart Example...

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Lecture Sections Objectives Assignment 9 2.4 The Product and Quotient Rule 2.4: 1-37 eoo. 39, 43, 45,47 Understanding Goals: 1. To understand how to use the Product Rule and Quotient Rule to find the derivatives of functions. 2. To be able to simplify derivatives. 3. To understand the meaning of derivative and use it to answer questions about real-life situations. Note: [ ] ( ) ( ) '( ) '( ) d f x g x f x g x dx f Example 1 : Differentiate the following functions: (a) 2 ( 2)( 5) y x x = + + (b) 1 ( ) 1 ( 1) f x x x = + - (c) 5 2 1 ( 3 ) y x x x = - 1
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Note: ( ) '( ) ( ) '( ) d f x f x dx g x g x ° Example 2 : Differentiate the following functions: (a) 1 2 3 x y x - = + (b) 1 3 ( ) 5 x f x x - = + 2
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(c) 2 3(3 2 ) 7 x x y x - - = Example 3 : Find the equation of the tangent line to the graph of 5 ( ) ( 2) 1 x g x x x - = + + when 0 x = . 3
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Example 4 : As blood moves from the heart through the major arteries out to the capillaries and back through the veins, the systolic pressure continuously drops. Consider a person whose blood pressure P (in millimeters of mercury) is given by 2 2 25 125 , 0 10 1 t P t t + = + where
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Unformatted text preview: after blood leaves the heart? Example 5 : It is possible for one medication to reduce the effectiveness of other medicines taken simultaneously. If a patient taking an antibiotic also takes a kaolin-pectin medication for diarrhea, the antibiotic adsorbs to the surface of the kaolin particles and passes out of the body. The amount of antibiotic available to the body is reduced. Suppose the adsorption coefficient for the amount of antibiotic adsorbed to the kaolin particles is given by: 16 ( ) 2 C A C k C = + where C represents the resulting concentration of antibiotic in the blood plasma (mg/dL), A represents the adsorption coefficient of antibiotic (mg of antibiotic/g of kaolin-pectin mixture), and k is a constant. Find an equation that represents the rate of change of the adsorption coefficient. 4...
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