Exam 3

Question 1

How do you find absolute extrema in optimization?

Answer 1

1. Take the derivative
2. Find critical values
3. Plug those into the equation along with the given greater than/equal than to find the points
4. Lowest y value - abs min, highest y value - abs max

Question 2

How can you find absolute extrema given an x>< 0 or in a word problem

Answer 2

1. Take the derivative
2. Find critical values
3. Take the second derivative
4. Plug the CV in it to find if it is concave up/down
5. Can label as max or min depending if up or down

Question 3

Average cost formula

Answer 3

A(q) = C(q)/q

Question 3

What is the formula for expressing demand as a function of d for elasticity?

Answer 3

(-p/function)(derivative of function)

Question 3

When given a profit problem, how do you set up the equation when the price is increased?

Answer 3

( x - price from distribution)(units sold now - how many units less ( x - retail price))

Question 4

Elasticity rules

Answer 4

x > 1 elastic
x = 1 unit elastic
x < 1 inelastic

Question 5

How do you do practical optimization given a rectangle problem?

Answer 5

1. Use perimeter and area formulas with information
2. Substitute so there is one variable
3. Find the derivative and get the CV
4. Plug the CV into the second derivative to find if it is a min or max

Question 6

How do you do practical optimization given a cost minimization problem?

Answer 6

1. Add all the costs together
   - Ordering fee means the fee times the units over x
   - cost of each is units x price
   - storage cost means cost times x/2
2. Take the derivative; the critical value will be the answer, and verify with the second derivative

Question 7

Basic expotent concept

Answer 7

Get the same base so they can cancel out, and you can solve for x

Question 8

Compound Interest

Answer 8

B = P( 1 + r/k ) to the kt
P = principal
r = annual interest rate
k = number of times a year interest is compounded
t = time in years
B = balance after t years

Question 9

Continuous Compound Interest

Answer 9

B(t) = Pe to the rt

Question 10

If f(x) = e to the x, then f’(x) =

Answer 10

e to the x

Question 11

If f(x) = e to the f(x), then f’(x) =

Answer 11

e to the f(x) times f’(x)

Question 12

If f(x) = lnx, then f’(x) =

Answer 12

1/x

Question 13

If f(x) = lnf(x), then f’(x) =

Answer 13

1/f(x) times f’(x)

Question 14

What should you do give ln of a fraction or sections multiplied together?

Answer 14

Use logarithmic rules

Question 15

What should you do given a fraction or series that you could use ln on?

Answer 15

1. Multiply both sides by ln
2. Break apart using log rules
3. Take the derivative
4. Multiply both sides by y

Question 16

When a question asks about rate or change, what should you do?

Answer 16

Take the derivative

Question 17

How can you find the percentage rate

Answer 17

Q’(t)/Q(t) times 100

Question 18

How do you get a level of production for which the average cost is minimized?

Answer 18

Set C(x)/x equal to C’(x) and solve for x

Question 19

What is marginal cost?

Answer 19

The derivative

Question 20

How do you graph ex/log functions?

Answer 20

1. Determine x and y intercepts
2. Determine asymptotes
3. Determine first derivative and make sign chart
4. Determine second derivative and make sign chart

Question 21

What does long run or very experienced mean?

Answer 21

Take the limit (ratio of leading coefficients

Question 22

When solving for x, what should you keep in mind?

Answer 22

Multiply it by whatever value it represents

Question 23

Backup for cost problem

Answer 23

square root of (2 x demand x ordering cost/cost per unit per year