Methods of Calculus, MAC3233 Final Exam April 28, 1993
Instructions:
Do not write your answers on this paper, use separate answer sheets. This is a closedbook
test. No calculators are allowed to be used. Time limit: 2.75 hours.
(1) (10 points) Diﬀerentiate:
f
(
x
) = 4(9
x
7
+ 2
x

5)

3
(2) (15 points) Find the equation of the tangent line to the graph of
f
(
x
) = 3 +
2
x
2
at
x
= 1.
(3) (20 points) For the function
f
(
x
) =

1
3
x
3
+ 3
x
2

5
x
(a) Give
f
0
(
x
) and
f
00
(
x
).
(b) Find all local extrema and classify each as a relative maximum or minimum.
(c) Find all inﬂection points.
(d) Sketch the graph.
(4) (20 points) Someone wants to build a 600squarefoot rectangular enclosure. Three sides of the
enclosure will be built of redwood fencing, at a cost of $8 per running foot. The fourth side will
be built of cinder blocks, at a cost of $16 per running foot. Find the dimensions of the rectangular
enclosure that will minimize the total cost of the building materials.
(a) Give the objective function.
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