EXERCISES 1-4 function on the given interval Find the local and absolute extreme values of the CAS 20. If f(x) ln(2x + x sin x), use the gr to estimate the intervals of increase and 1. fx) 1027x . [0, 4] of f on the interval (0, 15] 21. Investigate the family of functions f(x) What features do the members of this f mon? How do they differ? For which v 3. f(x)= [-2,0] , tinuous on )For which v graph at all? What happens as C â 4. f(x)-(In x)/y?" [1.3] ã 5-12 (a) Find the vertical and horizontal asymptotes, if any (b) Find the intervals of increase or decrease (c) Find the local maximum and minimum values (d) Find the intervals of concavity and the inflection points. (e) Use the information from parts (a)-(d) to sketch the graph 22. Investigate the family of functions f(x happens to the maximum and minimun inflection points as c changes? Illustrate by graphing several members of the far 23. For what values of the constants a and inflection of the curve y xax+ of f. Check your work with a graphing device 5. f(x) = 2-2x-x 24. Let g(x) f(x), where f is twice diff (x) > 0 for all x 0, and f is conca (-00, 0) and concave upward on (0ã0) (a) At what numbers does g have an ex 7, f(x) = x + v/ I-x (b) Discuss the concavity of g 12. y In(x21) 25-32 Evaluate the limit tan Ï.x 25. lim 26. lim 13-16 Produce graphs off that reveal all the important aspects of the curve. Use graphs of f' and f" to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and inflection points. In Exercise 13 use calculus to find these quantities exactly 27. lim 28. lim 13. f(x) 29. lim xe 30. lim 14. 15. ,f(x)-3x®-5x5 +x"-5x3-2x2 + 2 16, f(x)-sin x cost, 0
