Math

MA 141 Turn in homework 3.6

Pitts SHOW YOUR WORK! Name _______________________

1. (#14) Find dy/dx by implicit differentiation. x2 + 5xy + y2 = 10. Show your work

2. (#26) Find dy/dx by implicit differentiation 2 2 3

x y x

x y

 

 . (Hint: multiply both sides by LCD first.)

3. (Similar to # 32) Find an equation of the tangent line to the graph of the function 2 2

17y x  at (1, 4).

Show your work. Leave the equation in slope-intercept form of a line.

4. (#34) Find an equation of the tangent line to the graph of the function 3

( 1)x y x   at (1, -1). Show

your work. Leave the equation in the slop-intercept form of a line.

5. (#42) Suppose the quantity x of Super Titan radial tires made available each week in the marketplace

is related to the unit-selling price by the equation 21

48 2

p x  where x is measured in units of a

thousand and p is in dollars. How fast is the weekly supply of Super Titan radial tires being introduced

into the marketplace when x = 6, p = 66, and the price/tire is decreasing at the rate of $3/week?

6. (#44) Suppose the wholesale price of a certain brand of medium-size eggs p( in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the equation 625 p2 – x2 = 100. If 25,000 cartons of

eggs are available at the beginning of a certain week and the price is falling at the rate of 2

cents/carton/week, at what rate is the supply falling?

7. ( #52) Two ships leave the same port at noon. Ship A sails north at 15 mph, and ship B sails east at 12 mph. How fast is the distance between them changing at 1 p.m.?

8. Suppose that for a company manufacturing calculators, the cost and revenue equations (in $) are:

90, 000 30C x  and 2

300 30

x R x  , where the production output in 1 week is x calculators,

a.) Write the Profit equation.

b.) If production is increasing at a rate of 500 calculators per week when production output is 6,000 calculators, find the rate of increase (decrease) in the profit.