math final 2007 fall

60 per television 10 d 2 x y 3 dx 5 3 x y2 dy dx mt y

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Unformatted text preview: x 0.09 x 2 50 x (the revenue function) (b) R x x p x 0.09 x 50 (c) R x 0.18 x 50 0.18 150 50 23 R 150 If the level of production is 150 units then the (approximate) marginal revenue is $23.00 . 12. (a) f x3 3 x 2 x f x x2 x 3 0 at x increasing for x 3, 0 (the critical values). 3 ; decreasing for (b) Relative maximum point (c) f 3x 2 6 x x 3 x 0 and for x 0 . 3, 11 . No relative minimum point. 4 3x x 2 f x 0 at x 2, 0. f concave down for x 2 and x 0 ; concave up for 2 x 0 (d) The inflection points are 2 , 0 and 0, 4 . 13. f x 3x 2 18 x 24 3 x 4 x 2 f x 0 at x 4 and at x 2 The only critical value in the given (closed) interval is 2 . f 3 7 ; f 2 5 ; f 4 329 The absolute minimum point is 2 , 5 , and the absolute maxim...
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