April 21
section covered in text:
Section 4.1. Related Rates
objective:
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to be able to formulate and solve related rates problems
key ideas and/or vocabulary
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related rates, chain rule, implicit differentiate
strategies
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What quantities are given in the problem?
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What is the unknown?
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Draw a picture of the situation for any time t.
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Write an equation that relates the quantities.
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Finish solving the problem.
solved problems - using key ideas
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related rates of volume and length of cube, #1
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related rates of distance and speed, #5
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related rates of altitude and area of a triangle, #11
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related rates of volume and pressure, #21
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related rates of angular velocity and distance, #27
group work
begin work on homework assignment
announcements
Homework. #2,4,6,10
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QUESTION OF THE DAY
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Suppose C(r) is the total cost of paying
off a car loan borrowed at an annual interest rate of r%. What are
the units of C'(r)? What is the practical meaning of C'(r)?
What is its sign?
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SOLUTION
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SOLUTION.
The units of C'(t) are dollars per unit interest
rate.
The practical meaning meaning of C'(r) is
the change in the total cost of a loan as the interest rate changes.
The sign of C'(r) is positive since a higher
rate of interest on a loan means the toatl loan payments will be greater.
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