Math 1100
Homework 4
6 September, 2013
Name:
1. (5 points) If f (x) = 8x − x2 , compute f 0 (x).
2. (5 points) If f (x) = 8x − x2 , compute f 0 (3).
3. (5 points) Find the equation of the line tangent to the graph of f (x) = 8x − x2 at the
point (3, 15).
4. (5 points) Suppose the height of a ball in feet after t seconds is given by h(t) = 8x − x2 .
What is the velocity of the ball after 3 seconds? 1
5. (5 points) Suppose the profit of a paint company is given by P (x) = 8x − x2 where x
is the number of gallons of paint sold2 . What is the marginal profit if three gallons of
paint are sold?
1
If the poor physics in this problem bothers you, imagine you are throwing balls on a planet with
gravity of earth.
2
If your business has this profit function, you should consider finding a new occupation.
1
16
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