Final Flashcards
What kind of function is a one to one function?
A function where there is only one y value for every x value; when the function is either increasing or decreasing
Is a parabola or a function with relative min or max a one to one?
No because the curve makes it not one to one (ie fails horizonal line test). Saddle points would mean its a one to one
How do you find the inverse function?
By interchanging the values ie switch x and y
How do you find out if two functions are inverse functions using the composition property?
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.
How do you do growth and decay rates
Use the formula : P= the number of the population times (1-the rate)^number of years
Its 1- the rate if its decreasing
How do you find linear regression?
Store some values and then get that expreg from F5
What do you do when you have to solve for consumer surplus
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
How to find present value
Present value = the sum of money * ((1 - e^(-rt))/r)
How to find final value
The presenr value * e^(intrrest rate * years)
How to find critical points
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
Does this function have any critical points? 1/x?
No. So doesnt 1/(x+1) or things that look like that because apparently it can easily become a zero as a denominator.
How do you find the largest possible product? Of x and y?
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)
What do they do when they ask you to maximize revenue?
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)
How to tell if something is a relative max or min?
Take the second derivative and check for positive or ngative
How do you find max or min average cost?
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
True or false, marginal cost = average cost
True
How do you find out maximum profit
You have to do R(x) - c(x) then differentiate and critical points
Marginal revenue?
Derviative of revenue
Mrginal cost?
Derivative of cost
Elasticity of demand
Is p/x *dx/dp
Dx/dp is just ther derivative of x
If bacteria is decaying do you add a negative to the exponent in a=pert
Yah