136.152: Test #4 Solutions

20 minutes

Name:_____________________ Student Number: _______

1. At what point of the graph of the slope of the tangent line is equal to 11? Show your work.

gives the slope of the tangent at any point. Want to find such that the slope is 11, i.e., we want to solve . The solution is , and the point we wanted is (5,30).

2.  Find . (Do NOT simplify)

(a)

Product Rule (and a bit of Chain Rule):

(b)

Quotient Rule

(c)

, so, by the Chain Rule: .

3. Suppose the price and the demand are related by the formula . Find the marginal revenue when .

The revenue is . So, the marginal revenue is , and so, it is 100 when x=10.