Problem 1: Tangent line

Find an equation of the tangent line to graph of

y = x3 – 2x +1 at the point (1,0). Graph

both the function and the tangent line on the same screen.

Problem 2: Consumption function

If the consumption function is given by:

C = 20

I + 0.5

I 3  – 0.4I

Determine the marginal propensity to consume and the marginal propensity to consume to save when I = 100

Problem 3: Marginal cost

If the total cost function for a manufacturer is given by

6q2

c =          + 6000

q + 2

Find the marginal cost function.

Problem 4: Marginal revenue

If the demand function is given by

p =      25    

ln(q + 2)

Find the marginal revenue function.

Problem 5: Rate of return

To erect an office building, fixed cost are $1.44 million and include land, architect’s fee, a basement, a foundation and so on. If x floors are constructed, the cost (excluding fixed cost) is:

c = 10x éë120, 000 + 300 ( x -1)ùû

The revenue per month is $60,000 per floor.  How many floors will yield a maximum rate of return on investment? (Rate of return = total revenue/ total cost)

Problem 6: Elasticity of Demand

The sole producer of a product has determined that the marginal revenue function is:

dr = 100 – 3q2

dq

Determine the point elasticity of demand for the product when q = 5 (Hint:  First find the demand function).

Problem 7: Total cost

A manufacturer’s marginal cost function is

dc = 0.004q2 – 0.5q + 50

dq

If c in dollars, determine the cost involved to increase production from 90 to 180 units.