Chem

CALCULUS FOR BUSINESS TEST 2

1. f(x) = 5x4 ln x 1.

2. fx=2x + 35x + 1 2.

Use the chain rule to find the derivative and simplify.

3. f(x) = (3x2 – 4x)6 3.

4. y = ln(x2 + 9x) 4.

5. gx=4x-5 5.

6. fx= 4ex2-5 6.

CALCULUS FOR BUSINESS TEST 2 page 2

7. Find the equation of the tangent line to the graph 7.

of f at x = 2.

fx=2x + 13x - 1

8. The number x of bicycle helmets people are willing to buy

per week from a retail chain at a price of $p is given by

x=1,000-60p+25 , 20 ≤p ≤100 8a.

a. Find dx/dp 8b.

b. Find the instantaneous rate of change of demand

with respect to price when the price is $75.

Use implicit differentiation to find y’ and evaluate y’ at the indicated point.

9. y2 – y – 4x = 0; (0, 1) 9.

10. 2x3 y – x3 + 5 = 0; (-1, 3) 10.

CALCULUS FOR BUSINESS TEST 2 page 3

11. x ey − y = x2 – 2; (2, 0) 11.

12. 3xy – 2x – 2 = 0; (2, 1) 12.

13. x2y – 3x2 – 4 = 0; (2, 4) 13.

14. x3 – y = ln y; (1, 1) 14.

15. Find the equation of the tangent line to the graph of 15.

the equation at the indicated point

xy2 – y – 2 = 0; (1, 2)

CALCULUS FOR BUSINESS TEST 2 page 4

16. The drug concentration in the bloodstream t hours 16.

after injection is given approximately by

C(t) = 5e-0.3t

where C(t) is concentration in milligrams per milliliter.

Find the rate of change of concentration after 3 hours.

17. The price p (in dollars) and demand x for a product are 17. dx/dt

related by

2x2 + 5xp + 50p2 = 80,000

If the price is increasing at a rate of $2 per month when

the price is $30, find the...