6. An observer is 1000 feet from a point where a projectile is fired vertically upward at a constant velocity of 100 ft/sec. What is the rate of change of the angle of elevation of the projectile when it is radians above the horizontal?

a) 0.4 rad/sec

b) rad/sec

c) 0.05 rad/sec

d) 0.1 rad/sec

e) none of these

7. What is the smallest slope that the tangent line to the curve y = x5 + 2x can have?

a) 0

b) 2

c) 5/2

d) 2/5

e) none of these

8. Suppose that the function is twice differentiable on the open interval I containing the critical point c at which . Which of the following must be true?

a) there is an inflection point at c,

b) there is a local minimum at c,

c) there is a local maximum at c,

d) the function is constant on I,

e) none of the above.

9. Find the limit of f as x approaches 5 from the right given f(x) = .

a) 1

b) -1

c)

d)

e) none of these

10. Let f be a function that has a continuous derivative on [a, b], f(a) and f(b) have opposite signs, and f '(x) 0 for all numbers x between a and b, (a < x < b). How many solutions does the equation f(x) = 0 have ( a < x < b)?

a) 1

b) 0

c) 2

d) cannot be determined

e) none of these

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