Math 180 Business Calculus

chapter 4

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1.RevenueAnalysis. From our textbook,on page 252do problem #92

2.Price Analysis.From our textbook, on pages 252/253do problem #94

3(a).Graphing Strategy. Determine the interval on which the graph of each function is concave upward and/or concave downward. Sketch the graph of each function.

(i)f(x) = -e-x(ii)h(x) = x5

3(b) Find the inflection point(s) ofx4- 2x3- 36x+12

4. Evaluate(a) lim -3x2x(b) lim 5e-4x(c)lim ln(x+2)

xxx-2+

(d) lim (e -ex)/ (x-1)(e) lim x/ex(f) lim(lnx)/x3

x1xx

5.Graphing Technique: Consider the functionR(x)=x2+ x - 6

x2- x - 12

(i)Find the domain(ii) Find the x-intercept(iii) Find the y-intercept

(iv) Find the HorizontalAsymptote(v) Find the Vertical Asymptote

(vi) AnalyzeR'(x)to find the critical value(s)ofR(x) and the partition number(s) ofR'(x). Draw a sign Chart to determine the interval of decrease and the interval of increaseand any extrema.

(vii)AnalyzeR''(x)to find the partition numbers (if any) for R''(x). Draw a sign chart to determine the interval(s) off up-concavity, and down concavity. Locate any inflection point.

(viii)Sketch the graph ofR(x)

6.Extrema:

(a)Find the absolute maximum and minimum , if either exists , for the given function in the indicated interval.

x2-6x+ 7on [0 , 10]

(b)Use the second derivative test to find local maxima and minima of the functionbelow.

x3-9x2+ 24x -10

7.Optimization:

(a)Find two numbers whose sum is 21 and whose product is a maximum.

(b)Find the dimension of arectanglewith an area of 108 square feet that has minimum perimeter.

8.Ahome owner has $480 to spend on building a fence around a rectangular garden . The north and the south opposite sides of the fence are to be constructed with wood fencingcosting $8 per linear foot. The east andthe west oppositesides of thefence will be constructed with wireat acost of $4 per linear foot.Find the dimensions and the area of the largest garden that can be enclosed with $480 worth of fencing.

9.An office supply company sells xheavy duty paper shredders per year at $p per shredder. The price demand equation for these shredders is

p = 400 -x/40

(a)What price should the company charge for the shredders to maximize revenue?

(b)What is the maximum revenue?

10. A college student center sells 1,000 cups of coffee per day at aprice of $2.40.

A market survey shows that for every $0.05reduction in price,50more cups of coffee will be sold. How much should the student center chargefor a cup of coffeein order to maximize revenue?