Math 115 Test 2 5 pts each October 29, 1996

1. What information does a horizontal asymptote give you about a function?

2. What information does a vertical asymptote give you about a function?

Find all HA's & VA's

3. f(x) = (x-1)(x-3)

4.

5. If and f'(x) is negative for all x:

a) what is ? (Assume this limit exists.)

b) Draw this function

6. Give the graphical definition of the derivative of y = f(x) at the point (a, f(a)). You must use a complete sentence to get any credit at all.

7. Give the algebraic definition of the derivative of y = f(x) at the point (a, f(a)). You must use a complete sentence to get any credit at all.

8. At what point(s) does y = (x-3)³(x-2)¹² have a horizontal tangent ?

9. When do you NOT use the quotient rule when differentiating a fraction?

Differentiate:

10. f(x) =

11.

12. x = t^-2/3 - 4t^1/3

13.

14.

15. f(x) = x(3x-2)⁶

16.

17.

18. y = (x^-2 + x^-1)^-3

19.

20.