Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 40. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | Exploratory Problems for Chapter 10 371 21. The graph below shows the total cost and total revenue curves for a certain flrm. Both revenue and cost are functions of q where q represents quantity. Proflt Total Revenue - Total Cost R q - C q a Draw a graph of proflt against quantity labeling the points 21 Q2 Q3 and 24. b What do the quantities Q1 Q2 Q3 andQ4 mean as far as the proflts are concerned c Is the slope of the revenue curve constant or does it vary with q Interpret the slope of the revenue curve in terms of the economic model. Economists call the slope of the revenue curve the marginal revenue. d Is the slope of the cost curve constant or does it vary with q Interpret the slope of the cost curve in words. Economists call the slope of the cost curve the marginal cost. e Draw a set of axes with the vertical axis labeled item and the horizontal axis labeled q for quantity items produced and sold . On this set of axes sketch both R q and C q . f Verify by looking at the accompanying graph that proflt is a maximum or a minimum when the slope of the cost curve is equal to the slope of the revenue curve. How does this follow from the flrst derivative test g Bonus especially for those interested in economics Explain in words why it makes sense in economic terms that proflt is a maximum or a minimum when the slope of the cost curve is equal to the slope of the revenue curve. R A Portrait of Polynomials and Rational Functions Linear functions quadratics and cubics are all members of the larger family of polynomial functions a family whose members are functions that can be written in the form x a0 aix 2 2 --------1- a xn where a0 a1 a2 . a are all constants and the exponents of the variable are nonnegative integers. We have already looked carefully at linear and quadratic functions in this chapter we will look at characteristics of higher-degree polynomials so that we know what to expect of them. We ll begin with a case study of cubics both because we have run into .
