Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 23. 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 | Qualitative Interpretation of the Derivative 201 d f graph off 0 sign off 0 f e graph off -1 T- sign of f 0 - 0 As you can see vertically shifting the graph of f doesn t change its slope. EXERCISE Given the graph of f sketch the graph of f . Include a number line indicating both the sign of f and the direction of the graph of f. EXERCISE Given the graph of f sketch two possible graphs of f. Make one of these graphs pass through the origin. 202 CHAPTER 5 The Derivative Function PROBLEMS FOR SECTION 1. Below is a graph of f not f. Although the graph is of f the questions we ask are about f. a For what values of x in the interval 0 5 is the graph of f increasing b For what values of x in the interval 0 5 is the graph of f decreasing c Where on the interval 0 5 is the value of f x the smallest 2. Below is a graph of g not g. Although the graph is of g the questions asked are about g. a For what values of x in the interval -2 6 is the graph of g increasing b For what values of x in the interval -2 6 is the graph of g decreasing c Where on the interval -2 6 is the value of g x the smallest 3. On the following page match each of the eight graphs a-h with the correct graph A-H of its slope function . its derivative. When you have completed your work on this problem compare your answers with those of one of your classmates. If you disagree about an answer each of you should discuss your reasoning to see if you can come to a consensus on the answers. Qualitative Interpretation of the Derivative 203 ABC y y y f y Gy Hy 4. The graph of g x x2 - 4 looks just like the graph of x x2 shifted vertically downward 4 units. Will and g be the same or different Explain your reasoning. For Problems 5 through 8 sketch the graph of . 5. .
