ECN 504 Lecture Notes - Lecture 1: Partial Derivative

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olivemink212

30 May 2015

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Compute the first derivative and second derivative of the following functions: a. ) f(x) = 6x + 1. 32x + b. ) f(x) = c. ) f(x) = (2+x)(3-x) d. ) f(x) = 7 e. ) f(x) = 6ln(x) f. ) f(x) = ax2 bx3 g. ) f(x) = 2. Compute the first derivative of the following functions: where a and b are constants. 4/1x + 4 a. ) f(x,y) = b. ) f(x,y) = c. ) f(x,y) = d. ) f(x,y) = [ 36x y + 3xy + 4y + x + 4+ xy. 32x ln(2xy)][ xy ln x y y x. 2)]1 yx a. ) f(x) = b. ) f(x) = c. ) f(x) = Compute the value of x that maximizes or minimizes the following functions and find the maximum/minimum value of the function. Show that this is indeed a maximum/minimum by evaluating the second derivative of the function: a. ) f(x) = 4 2x - 2x +12 b. ) f(x) = 25ln(3x) 5x + 1000 c. ) f(x) =

Related Questions

QUESTION 1

Assume there are two basic goods produced in a nation, consumer goods and capital goods. The production possibilities graph for these two goods is bowed out from the origin. This reason for this shape of the graph is because of:

	A.	the other-things-equal assumption.
	B.	the law of increasing opportunity costs.
	C.	diminishing marginal utility.
	D.	present choices and future possibilities.

1 points

QUESTION 2

From an economic perspective, when a student decides to attend another year of college, the student has concluded that the:

	A.	marginal costs of attending college are reduced by the availability of grants and subsidies.
	B.	marginal benefits of attending college have increased because the future is brighter.
	C.	marginal benefits of attending college are greater than the marginal costs.
	D.	marginal costs of attending college have decreased to make college affordable.

1 points

QUESTION 3

A person observes that as consumer prices fall, economic growth increases. The person concludes that fall consumer prices leads to economic growth. This conclusion would be an example of:

	A.	confusing correlation with causation.
	B.	the fallacy of composition.
	C.	trade-offs among economic goals.
	D.	the other-things-equal assumption.

1 points

QUESTION 4

The problem of unlimited wants and limited income is known as

	A.	the scientific method.
	B.	unequal wealth distribution.
	C.	normative economics.
	D.	the economizing problem.

1 points

QUESTION 5

A point outside the production possibilities curve is:

	A.	unattainable without economic growth.
	B.	attainable and the economy is efficient.
	C.	unattainable without inflation.
	D.	attainable, but the economy is inefficient.

1 points

QUESTION 6

Which one of the following would be an example of loaded terminology?

	A.	market forces
	B.	tentative hypothesis
	C.	entrepreneurial functions
	D.	creeping socialism

1 points

QUESTION 7

Suppose there are two economies, Alpha and Beta, both of which have the same production possibilities curves. If Beta devotes more resources to produce investment goods than consumer goods as compared to Alpha, then in the future:

	A.	Alpha will not be able to achieve full employment.
	B.	Beta will not be able to achieve full employment.
	C.	Alpha will experience greater economic growth than Beta.
	D.	Beta will experience greater economic growth than Alpha.

1 points

QUESTION 8

Macroeconomics, as opposed to microeconomics, is concerned with

	A.	individual businesses.
	B.	new computer technology.
	C.	the stock market.
	D.	the economy as a whole.

1 points

QUESTION 9

Which one of the following is an example of a positive economic statement?

	A.	The size of the Federal government should be reduced.
	B.	Midwest states affected by drought should be given more federal disaster aid.
	C.	Education and income are highly correlated.
	D.	The minimum wage for workers should be raised to help low-income workers.

1 points

QUESTION 10

Economics is primarily concerned with

	A.	interactions between the government and market participants.
	B.	how scarce resources are used.
	C.	the production and distribution of capital goods.
	D.	how income is divided among individuals.

1 points

QUESTION 11

The production possibilities table below shows the hypothetical relationship between the production of guns (national defense) and butter (social goods) in an economy.

A B C D E

Guns 0 4 7 9 10

Butter 4 3 2 1 0

If the economy is producing at alternative C, what is the opportunity cost of producing another unit of butter?

	A.	3 units of guns.
	B.	1 units of guns.
	C.	2 units of guns.
	D.	4 units of guns.

1 points

QUESTION 12

Assume that a consumer can buy only two goods X and Y, and has an income of $120. The price of X is $10 and the price of Y is $20. If the consumer spends all of her money on X and Y, which of the following would be a possible combination:

	A.	4X and 2Y
	B.	5X and 3Y
	C.	6X and 3Y
	D.	8X and 1Y

1 points

QUESTION 13

In the production possibilities model of an economy, when there is full employment of resources

		a nation will be operating at an interior point within its production possibilities curve.
		a nation will be operating on the production possibilities curve.
		the production possibilities curve will shift outward to the right.
		the production possibilies curve will shift inward to the left.

1 points

QUESTION 14

In economics the concept that there is "no free lunch" means

	A.	scarce resources were used to produce these "free" goods so there is an opportunity cost to producing them.
	B.	consumers are irrational when they ask for a free lunch unless they can make the case that the free lunch benefits business.
	C.	the marginal cost of the "lunch" is greater than the marginal benefit.
	D.	businesses could not make a profit if they gave away free goods to consumers.

1 points

QUESTION 15

Assume that a consumer can only purchase two goods with her income. A straight-line budget constraint indicates that the opportunity cost of obtaining an additional unit of one good is:

	A.	negative.
	B.	constant.
	C.	increasing.
	D.	decreasing.

carmineferret43

QUESTION 1

	A.	the other-things-equal assumption.
	B.	the law of increasing opportunity costs.
	C.	diminishing marginal utility.
	D.	present choices and future possibilities.

1 points

QUESTION 2

From an economic perspective, when a student decides to attend another year of college, the student has concluded that the:

	A.	marginal costs of attending college are reduced by the availability of grants and subsidies.
	B.	marginal benefits of attending college have increased because the future is brighter.
	C.	marginal benefits of attending college are greater than the marginal costs.
	D.	marginal costs of attending college have decreased to make college affordable.

1 points

QUESTION 3

A person observes that as consumer prices fall, economic growth increases. The person concludes that fall consumer prices leads to economic growth. This conclusion would be an example of:

	A.	confusing correlation with causation.
	B.	the fallacy of composition.
	C.	trade-offs among economic goals.
	D.	the other-things-equal assumption.

1 points

QUESTION 4

The problem of unlimited wants and limited income is known as

	A.	the scientific method.
	B.	unequal wealth distribution.
	C.	normative economics.
	D.	the economizing problem.

1 points

QUESTION 5

A point outside the production possibilities curve is:

	A.	unattainable without economic growth.
	B.	attainable and the economy is efficient.
	C.	unattainable without inflation.
	D.	attainable, but the economy is inefficient.

1 points

QUESTION 6

Which one of the following would be an example of loaded terminology?

	A.	market forces
	B.	tentative hypothesis
	C.	entrepreneurial functions
	D.	creeping socialism

1 points

QUESTION 7

	A.	Alpha will not be able to achieve full employment.
	B.	Beta will not be able to achieve full employment.
	C.	Alpha will experience greater economic growth than Beta.
	D.	Beta will experience greater economic growth than Alpha.

1 points

QUESTION 8

Macroeconomics, as opposed to microeconomics, is concerned with

	A.	individual businesses.
	B.	new computer technology.
	C.	the stock market.
	D.	the economy as a whole.

1 points

QUESTION 9

Which one of the following is an example of a positive economic statement?

	A.	The size of the Federal government should be reduced.
	B.	Midwest states affected by drought should be given more federal disaster aid.
	C.	Education and income are highly correlated.
	D.	The minimum wage for workers should be raised to help low-income workers.

1 points

QUESTION 10

Economics is primarily concerned with

	A.	interactions between the government and market participants.
	B.	how scarce resources are used.
	C.	the production and distribution of capital goods.
	D.	how income is divided among individuals.

1 points

QUESTION 11

The production possibilities table below shows the hypothetical relationship between the production of guns (national defense) and butter (social goods) in an economy.

A B C D E

Guns 0 4 7 9 10

Butter 4 3 2 1 0

If the economy is producing at alternative C, what is the opportunity cost of producing another unit of butter?

	A.	3 units of guns.
	B.	1 units of guns.
	C.	2 units of guns.
	D.	4 units of guns.

1 points

QUESTION 12

	A.	4X and 2Y
	B.	5X and 3Y
	C.	6X and 3Y
	D.	8X and 1Y

1 points

QUESTION 13

In the production possibilities model of an economy, when there is full employment of resources

		a nation will be operating at an interior point within its production possibilities curve.
		a nation will be operating on the production possibilities curve.
		the production possibilities curve will shift outward to the right.
		the production possibilies curve will shift inward to the left.

1 points

QUESTION 14

In economics the concept that there is "no free lunch" means

	A.	scarce resources were used to produce these "free" goods so there is an opportunity cost to producing them.
	B.	consumers are irrational when they ask for a free lunch unless they can make the case that the free lunch benefits business.
	C.	the marginal cost of the "lunch" is greater than the marginal benefit.
	D.	businesses could not make a profit if they gave away free goods to consumers.

1 points

QUESTION 15

Assume that a consumer can only purchase two goods with her income. A straight-line budget constraint indicates that the opportunity cost of obtaining an additional unit of one good is:

	A.	negative.
	B.	constant.
	C.	increasing.
	D.	decreasing.

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ECN 504 Lecture Notes - Lecture 1: Partial Derivative

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