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The second exam for math 211 c, covering topics such as finding derivatives, analyzing graphs, and cost-revenue functions. Students are required to find derivatives of given functions without simplifying, determine the coordinates of a relative extreme point on a graph, and calculate the profit function and marginal profit from cost and revenue functions.
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Prof. J. Beachy 10/18/02 Circle recitation time: T 10:00 T 11:00 Th 11:
NO CALCULATORS! Be sure to show all necessary work.
(a) f (x) = (x^4 − 3 x^2 + 2x + 1)^8
(b) f (x) = (x^2 + 1)^3 (x^2 − 1)^2
(c) (p163 #33) f (x) =
x^2 − 1 x^2 + 1
(d) (p163 #37) f (x) =
4 x + 3 √ x
(e) (p172 #35) f (x) =
x^2 + 1 x^2 − 1
x^2 + 1
has one relative extreme point. Find the
coordinates of this point, and use the sign of f ′(x) to determine whether the point is a relative maximum or a relative minimum. You do not need to include a sketch of the graph.
2 x^2 x^2 − 16
, find (a) f ′(x) =
(b) critical points (if any); where the graph is increasing; where the graph is decreasing;
(c) the vertical and horizontal asymptotes.
(d) Given f ′′(x) =
192 x^2 + 1024 (x^2 − 16)^3
, find where the graph is concave up; concave down.
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