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Unformatted text preview: AP CALULUS BC
ASSIGNMENT #5
201617 DUE: Friday, December 16
TEACHER: Mrs. Dopkin You may work in groups but all members must hand in his/ her own paper. Be certain that all members of
your group understand the solutions to each question because a member of your group will be required to
present one of the problems. To expedite the correcting of this project, each problem needs to be completed neatly on a separate page.
This might mean recopying your work to make it a neater presentation. SHOW ALL WORK. Indicate
clearly the methods you use because you will be graded on the correctness of your methods as well as the
accuracy of your ﬁnal answers. Please clearly indicate the ﬁnal answer with a box or circle around it. It is not advised that you wait until the last night to begin this. It is designed to take a good amount of time. SECTION I: A graphing calculator is required for some problems or parts of problems on this section. If
you choose to use decimal approximations, your answer should be correct to three decimal places. 1. A man has 340 yards of fencing for enclosing two separate ﬁelds, one of which is to be a rectangle
twice as long as it is wide and the other a square. The square ﬁeld must contain at least 100 square yards and the rectangular one must contain at least 800 square yards.
a. If x is the width of the rectangular ﬁeld, what are the maximum and minimum possible values of x?
b. What is the greatest number of square yards that can be enclosed in the two ﬁelds? Justify your
answer. 2. A right circular cone and a hemisphere have the same base, and the cone in inscribed in the
hemisphere. The ﬁgure is expanding in such a way that the combined surface area of the hemisphere
and its base is increasing at a constant rate of 18 square inches per second. At what rate is the volume
of the cone changing at the instant when the radius of the common base is 4 inches? Indicate
appropriate units. (Note: The surface area of a cone is Ja‘l where r is the radius of the base and l is the slant height; the surface area of a sphere is 4m"? where r is the radius of the sphere.) 3. Consider the curve deﬁned by — 8x2 + 5xy + y3 = 149.
a. Find dy/dx.
b. Write an equation for the line tangent to the curve at the point (4, l).
c. There is a number It so that the point (4.2, k) is on the curve. Using the tangent line found in part (b), approximate the value of k.
d. Write an equation that can be solved to ﬁnd the actual value of It so that the point (4.2, k) is on the curve.
e. Solve the equation found in part (d) for the value of k. SECTION II: A calculator may NOT be used on this section. 4. A paIticle moves along the xaxis so that at any time t, its positions is given by x(t) = 2m + cos(2m‘).
a. Find the velocity at time t. b. Find the acceleration at time t.
c. What are the values of t, 0 5 t5 3, for which the particle is at rest? Justify your answer. d. What is the maximum velocity of the particle? . Let p and g be real numbers and let f be the function deﬁned by
ﬁx) 2 {1+2p(x—1)+(x—1)2forx S 1
qx + p f or x > 1
a. Find the value of q, in terms of p, for which f is continuous at x = 1.
b. Find the values of p and q for which f is differentiable at x = l. c. If p and (1 have the values determined in part (b), is f" a continuous function? Justify your
answer. . The ﬁgure below shows the graph of f ’(x), the derivative of a function f. The domain of the function f
is the set of all x such that 3 < x < 3.
a. For what values of x, 3 < x < 3, does f have a relative maximum? A relative minimum? Justify
your answer.
b. For what values of x is the graph of f concave up? Justify your answer.
0. Use the transformation found in parts (a) and (b) and the fact that 116) = 0 to sketch a possible
graph of f in a suitable domain. ' i ‘ Note: This is the graph of the derivative of f not the graph off. ...
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 Fall '17
 Mr. Dyke
 Calculus, Derivative, Continuous function, Mrs. Dopkin, AP CALULUS BC

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