Final

Question 1

What kind of function is a one to one function?

Answer 1

A function where there is only one y value for every x value; when the function is either increasing or decreasing

Question 2

Is a parabola or a function with relative min or max a one to one?

Answer 2

No because the curve makes it not one to one (ie fails horizonal line test). Saddle points would mean its a one to one

Question 3

How do you find the inverse function?

Answer 3

By interchanging the values ie switch x and y

Question 4

How do you find out if two functions are inverse functions using the composition property?

Answer 4

Plug one function into the other function for x, and then vice versa. If you get the same answer both times, they are inverse functions.

Question 5

How do you do growth and decay rates

Answer 5

Use the formula : P= the number of the population times (1-the rate)^number of years

Its 1- the rate if its decreasing

Question 6

How do you find linear regression?

Answer 6

Store some values and then get that expreg from F5

Question 7

What do you do when you have to solve for consumer surplus

Answer 7

Find the integral of the top functions over the interval and multiply it by the x and y values of the market equilibrium point (the poiint where the two functions equal each other)

For the producer surplus, we use the bottom function for the integral and We subtract it from the xy value (known as xe and pe) because its believed that the consumer surplus is derived by paying a lower than equilibrium price. Thus, the producer surplus is derived by taking xepe - the integral (the vice versa) because economists define producer surplus as the value derived by the producer chsrging a lower price

Question 8

How to find present value

Answer 8

Present value = the sum of money * ((1 - e^(-rt))/r)

Question 9

How to find final value

Answer 9

The presenr value * e^(intrrest rate * years)

Question 10

How to find critical points

Answer 10

Find the derivative. Then find what the denominator equals at zero AND what the numerator equals at zero. or if its factoraboe, what the factors (of the derivative!) are are at zero. To get the y, plug the x back into the original

Question 11

Does this function have any critical points? 1/x?

Answer 11

No. So doesnt 1/(x+1) or things that look like that because apparently it can easily become a zero as a denominator.

Question 12

How do you find the largest possible product? Of x and y?

Answer 12

Fiind the constraint so you can represent y or x in terms of the other term. Then find the vertex -b/2a , which gives you your value and then plug that back into the thing they need you to find (eg sum or product)

Question 13

What do they do when they ask you to maximize revenue?

Answer 13

Revenue is usually x*p, and p is the price or the demand function while x is the #of items.

So multiply p by x, find the derivative, then find what x is at the max (meaning set it to zero)

Question 14

How to tell if something is a relative max or min?

Answer 14

Take the second derivative and check for positive or ngative

Question 15

How do you find max or min average cost?

Answer 15

Do c(x)/x

Then differentiate and find critical poonts for max or min. Fnd out max and min using 2nd deriviative if you need it

Question 16

True or false, marginal cost = average cost

Answer 16

True

Question 17

How do you find out maximum profit

Answer 17

You have to do R(x) - c(x) then differentiate and critical points

Question 18

Marginal revenue?

Answer 18

Derviative of revenue

Question 19

Mrginal cost?

Answer 19

Derivative of cost

Question 20

Elasticity of demand

Answer 20

Is p/x *dx/dp

Dx/dp is just ther derivative of x

Question 21

If bacteria is decaying do you add a negative to the exponent in a=pert

Answer 21

Yah

Question 22

If if not compounded what do you use

Answer 22

Eg 30 dollars for 7 percent a year for 10 years is 30*(1.07)^10

Question 23

When something is added to the exponent does it shift left or right or up or down

Answer 23

It shifts left

Question 24

When do you use u substituitoon

Answer 24

When theres something complicated inside something simple for itnegrals

Question 25

What is the formula for present value

Answer 25

Principle *((1-e^(-rt))/r)

Question 26

What is the formula for elasticity of demand

Answer 26

P/x *dx/dp

Question 27

True or false: The derivative of e^(x^2-3x) is (e^(x^2-3x))*(2x-3)

Answer 27

True

Question 28

How to find average value

Answer 28

1/(b-a) * definite integrla of whatever they give you

Question 29

Horizontal asympototes, three conditions:

Answer 29

Top equation bigger-> none
Bottom bigger -> zero
Same size-> divide by the constant in front of the leading coefficients

Question 30

Vertical asympototes

Answer 30

Factor the denominator and set equal to zero

Question 31

Its concave up when

Answer 31

2nd derivative is positive in the interval

Question 32

It is concave down when

Answer 32

Second derivative is negative in the interval

Question 33

What to do with an exponential function with 2 points

Answer 33

Y=ab^x

Plug in one set of points for y and x. Try to find a in terms of b

Then plug in the second set using only one variable b

Solve for a, now you have a function

Question 34

True or false : d/dx of ((e^x)^10) is 10e^10x

Answer 34

True

Question 35

What is the log rule for loga(x^b)

Answer 35

B*loga(x)

Question 36

What can you do with ln(1/e^5)

Answer 36

Turn it into -5

Question 37

What is e^0?

Answer 37

1

Question 38

Formula for producer surplus

Answer 38

Xepe * integral of supply

(Xepe found by setting both equations equal to each other, solving for x, then plugging x into one of the equations for p)

Question 39

Frmula for consumer surplus

Answer 39

Intrgral of demand - xepe

Xepe found by equaling both euations to each other, solving for x and then plugging x into either for p

Question 40

Let y = 5 x^2. Find the change in y, \Delta y when x= 1 and \Delta x = 0.3 Find the differential dy when x= 1?
Let y = 5x^2.

Find the change in y, ∆y when x= 1 and ∆x = 0.3

Find the differential dy when x= 1 and dx = 0.3
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Answer 40

Best Answer: ∆y = 5(x + ∆x)^2 - 5x^2
= 5(x^2 + 2x∆x + ∆x^2) - 5x^2
= 5(2x∆x + ∆x^2)
= 10x∆x + 5∆x^2

So when x = 1 and ∆x = 0.3,
∆y = 1010.3 + 5*(0.3^2)
= 3 + 0.45
= 3.45

dy = 10x dx

So when x = 1 and dx = 0.3,
dy = 1010.3
= 3

Note: I have given you the answer you evidently wanted, but strictly speaking, dx and dy are differentials (infinitely small quantities) and as such cannot have real number values.
chauncy · 6 years ago
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Question 41

What do you do with that delta y stuff?

Answer 41

Every time you see an x, replace wth x+delta x, and at the end of that, subtract the original equation

Question 42

What is the chain rule for derivatives

Answer 42

Dy/du * du/dx

Basically if you have e^2x,you first find u which is 2x then find du which is 2. Then you take your y which is now e^u and find rhe derivstive of tht which is just e^u. Then you multiply your du with your dx. So yu get 2*e^u and then you plug in 2x for u.

Question 43

What is the derivstive of 4e^u?

Answer 43

4e^u

Nothing happens to the constant

Question 44

How to calculate net present value

Answer 44

A= p*((1-e^-n)/r

Ie all those ‘flows uniformly’ questions

Question 45

How to calculate actual change?

Answer 45

F(b) -f(a) on the interval a,b

Question 46

How calculare average rateof change

Answer 46

(F(b) - f(a)) /(b-a)

Question 47

What does closed interval mean?

Answer 47

Does include endpoints

Question 48

What does open interval mean?

Answer 48

Does not include endpoints

Question 49

When you see those interval problems what do you do?

Answer 49

Make a chart

Question 50

How do you do epsilon

Answer 50

((F(x+delta x) - f(x))/ delta x) -f’(x)

Question 51

What do you do with e to the exponent?

Answer 51

E to the exponent times the derivstive of the exponent

Question 52

Wat do you do when you see solve for dy/dx = somethig?

Answer 52

Multiply both sides by dx

Find the integral

Question 53

How do you tell if a function is increasing or decreasing?

Answer 53

Use the first derivative test. If the derivative is positive on that interval, it is increasing and if the derivative is negative on that interval, it is decreasing.