AP Calculus BC
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1.
2.
Applications of Derivatives Practice Name:
11-22-15
Let f (x)  12  x 2 for x  0 and f (x)  0 .
(a)
The line tangent to the graph of f at the point (k, f (k)) intercepts the x-axis at x  4 . What is the value of k?
(b)
An isosceles triangle whose base is the interval from (0, 0) to (c, 0) has its vertex on the graph of f. For what value
of c does the triangle have maximum area? Justify your answer.
Let f (x)  6  x 2 . For 0  w  6 . Let A(w) be the area of the triangle formed by the coordinate axes and the line
tangent to the graph of f at the point (w, 6  w 2 ) .
(a)
Find A(1) .
(b)
For what value of w is A(w) a minimum?
3.
In a swim-and-run biathlon, you must get to a point on the other side of a 50 m wide river, 100 m downstream from the
starting point. You can swim 2 m/sec and run 5 m/sec. Toward what point on the opposite side of the river should you
swim to minimize your total time?
4.
A new oil well 300 m from the road is to be connected to storage tanks 1000 m down the road from the well. Building
pipeline across the field cost $50/m, where building it along the road costs $40 per meter. How should the pipeline be laid
out in order to minimize the total cost?
5.
The figure provided represents an observer at point A watching balloon B as it rises from point C. The balloon is rising at a
constant rate of 3 meters per second and the observer is 100 meters from point C.
(a)
Find the rate of change in x at the instant when y  50 .
(b)
Find the rate of change in the area of right triangle BCA at the instant when y  50 .
(c)
Find the rate of change in  at the instant when y  50 .

HW: p. 274: 3, 7, 23, 28, 33, 39, 41, 44, 47, 49, 75, 77, 85, 91 AND p. 277: 1, 2, 4, 13, 16 AND p. AP4-1: 1, 3, 4, 6, 7, 8, 10