MATH 0120 Midterm: Math 0120 Exam 1 (0120) sln spring 2013-341
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S o l u t i o n s: [10 points] find and simplify the di erence quotient f (x + h) f (x) h for the function f (x) = 3x + 2. Solution: f (x + h) f (x) h. 3(x + h) + 2 (3x + 2) h. 3x + 3h + 2 3x 2 h. The pro t is p (x) = r(x) c(x) = 12x + 1 x2 4x 8. = x2 + 8x 7 = (x2 8x + 7) = (x 1)(x 7) = 0. The break-even points are x = 1 and x = 7. (b) [10 points] find the company maximum pro t. The parabola p (x) = x2 + 8x 7 opens downward. Hence the maximum pro t occurs at its vertex when x = b. Then the maximum pro t is p (4) = 16 + 32 7 = 16 7 = 9 million dollars.
