3.1 Increasing&DecreasingFunctions

3.1 Increasing&DecreasingFunctions - 1. Specify the...

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MAC2233 (3.1) FIU, MDC- North 3.1 Increasing & Decreasing Functions; Relative Extrema A function is increasing if  y  increases as  x  increases; it is decreasing if  y  decreases as  x  increases.  Relative  extrema are turning points in the graph: a relative maxima is where an increasing function reverses and  becomes a decreasing function (a peak); a relative minima is where a decreasing function reverses and  becomes an increasing function (a valley).  A function is increasing when  f ’(x)   > 0  and decreasing when  ‘(x) < 0 .  The only points where f(x) can have a relative extremum are where  f ‘(x) = 0  or  f ‘(x) does not  exist ; these points are called critical points if  x  is in the domain of f(x).  See blue box on page 190 for steps in  sketching the graph of a continuous function f(x) using the derivative f ‘(x).
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Unformatted text preview: 1. Specify the intervals on which the derivative of the given function is positive and those on which it is negative: Find the intervals of increase and decrease for the given function: 2. f(t) = t 3 + 3t 2 + 1 3. ( 29 ( 29 f x x x 2 2 2 1 1 1 1 =-+ + MAC2233 (3.1) FIU, MDC-North MAC2233 (3.1) FIU, MDC-North Determine the critical numbers of the function and classify each point as a relative maximum, relative minimum, or neither: 4. ( 29 =-f x x x 9 5. Use calculus to sketch the graph of the function: 6. The total cost of producing x units of a certain commodity is given by C(x) = x 5 2 3 + + . Sketch the cost curve and find the marginal cost. Does marginal cost increase or decrease with increasing production? MAC2233 (3.1) FIU, MDC-North...
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This note was uploaded on 01/04/2012 for the course MAC 2233 taught by Professor Royer during the Fall '08 term at FIU.

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3.1 Increasing&amp;amp;DecreasingFunctions - 1. Specify the...

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