Chat with AIExam 3: Differentiation
Exam 1: Preliminaries205 Questions
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Exam 3: Differentiation330 Questions
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Suppose 
measures an economy's personal consumption expenditure and x the personal income, both in billions of dollars. Then, 
measures the economy's savings corresponding to an income of x billion dollars. Then 
. The quantity dS/dx is called the marginal propensity to save.
For the consumption function 
, find the marginal propensity to save.
measures an economy's personal consumption expenditure and x the personal income, both in billions of dollars. Then, measures the economy's savings corresponding to an income of x billion dollars. Then . The quantity dS/dx is called the marginal propensity to save.
For the consumption function , find the marginal propensity to save. (Multiple Choice)
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(36) Find the derivative of the function by using the rules of differentiation. 
(Essay)
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(37) Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the equation 
.
If 23,000 cartons of eggs are available at the beginning of a certain week and the supply is falling at the rate of 800 cartons/week, at what rate is the wholesale price changing? Round the answer to the nearest tenth. (Hint: To find the value of p when 
, solve the supply equation for p when 
).
Round the answer to the nearest tenth, if necessary.
__________ 
.
If 23,000 cartons of eggs are available at the beginning of a certain week and the supply is falling at the rate of 800 cartons/week, at what rate is the wholesale price changing? Round the answer to the nearest tenth. (Hint: To find the value of p when , solve the supply equation for p when ).
Round the answer to the nearest tenth, if necessary.
__________ (Short Answer)
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(42) 
. Find 
given that 
, 
, 
, 
.
Find the derivative of the function by using the rules of differentiation. 
(Multiple Choice)
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(37) Determine whether the statement below is true or false. If the marginal profit function is negative at 
, then it makes sense to increase the level of production.
, then it makes sense to increase the level of production. (Multiple Choice)
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(35) 
Find the derivative of the function by using the rules of differentiation. 
(Multiple Choice)
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(36) 
Two ships leave the same port at noon. Ship A sails north at 21 mph, and ship B sails east at 15 mph. How fast is the distance between them changing at 1 p.m.?
(Multiple Choice)
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(34) Let f be the function defined by 
. Find the approximate change in y if x changes from 
to 
. Find the actual change in y if x changes from 
to 
.
. Find the approximate change in y if x changes from to . Find the actual change in y if x changes from to . (Multiple Choice)
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(42) A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is 
where x stands for the number of units produced. What is the actual cost incurred in manufacturing the 301st oven and the marginal cost when 
?
where x stands for the number of units produced. What is the actual cost incurred in manufacturing the 301st oven and the marginal cost when ? (Multiple Choice)
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. 
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