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Unformatted text preview: ar the ticket price is lowered, average
attendance will increase by 1000. How should the owners of
the team set the ticket price to maximize their revenue from
ticket sales? ; 60. A manufacturer determines that the cost of making x units of a
21. commodity is C x
1800 25x 0.2 x 2 0.001x 3 and the
demand function is p x
(a) Graph the cost and revenue functions and use the graphs to
estimate the production level for maximum proﬁt.
(b) Use calculus to ﬁnd the production level for maximum
(c) Estimate the production level that minimizes the average
cost. 47. By applying the Mean Value Theorem to the function fx x 1 5 on the interval 32, 33 , show that
s33 2 2.0125 48. For what values of the constants a and b is 1, 6 a point of x3 inﬂection of the curve y
49. Let t x ax 2 bx 1? 61. Use Newton’s method to ﬁnd the root of the equation 2 f x , where f is twice differentiable for all x,
0 for all x 0, and f is concave downward on
and concave upward on 0, .
(a) At what numbers does t have an extreme value?
(b) Discuss the concavity of t. x5 x4 3x2 3x
six decimal places. ,0 50. Find two positive integers such that the sum of the ﬁrst number 51. Show that the shortest distance from the point x 1, y1 to the By C 52. Find the point on the hyperbola x y 3x 53. Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius r.
54. Find the volume of the largest circular cone that can be inscribed in a sphere of radius r.
ABC, D lies on AB, CD AB, AD
5 cm. Where should a point P be chosen on CD
so that the sum PA
PC is a minimum? 1 correct to six decimal places. the function f t
places. cos t t 2 correct to eight...
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- Fall '07