Please only questions 1, 7, 11, 13Thank you
4.6 E EXERCISES 18 Produce graphs of f that reveal all the important aspects of the curve. In particular. you should use graphs of j" and f" to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and inection points. 1. x) = x5 51\"- x3 2813 2x 2. 1(x) = 2x\" + 5x5 + 14(1).3 110.:1 3. f(x) = x\" 5;" + 25x" x' 48.x 4 )__r'x.8 5 _)_ '4'.\" 1316 - 1\" x3+x1+l 6.](x}=6sin.r_r'l, 5$x3 T..f(x)=6sin_r+cotx. 1T$_rrr a. x) = e" [1.18m4 910 Produce graphs of f that reveal all the important aspects of the curve. Estimate the intervals of increase and decrease and intervals of concavity, and use calculus to nd these inter vals exactly. I 8 1 1 2x10\" 9. x=l++,+ 1o. x= 4'1) .1' X' X" 4'1) 1,; X" 111 2 (a) Graph the function. (b) Use l'Hospital's Rule to explain the behavior as x > 0. (c) Estimate the minimum value and intervals of concavity. Then use calculus to nd the exact values. 11. ,1 (x) = x'l ln .r 12. x) = xe'e 1314 Sketch the graph by hand using asymptotes and inter cepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values. +4 3' 13. fix) = (X \"Uni 1) ) 14-.x'Ir)= 2r+3 xZ ll!!! 15. If f is the function considered in Example 3. use a com puter algebra system to calculate f' and then graph it to conrm that all the maximum and minimum values are as given in the example. Calculate f" and use it to estimate the intervals of concavity and inection points. EB 16. If f is the function of Exercise 14. nd f\" and f " and use their graphs to estimate the intervals of increase and decrease and concavity of f. [3111 1722 Use a computer algebra system to graph f and to nd I ' and f Use graphs of these derivatives to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and inflection points of f. 17 _}_ x"+5_x-'+t '1\" x4+_r-'x2+2 2m 18. 'x = ) l+x+x' 19' x} = V'x + 5 sin x. x g 20 20. fix) = x tan'(x3) . l_el.a".t 21. j(x}=J,_' ["9\" 22 I) 3 . x = j 3--2sinx 2324 Graph the function using as many viewing rectangles as you need to depict the true nature of the function. 23. x) = l coslr ) .1"; 24. x} = e' + ln|x 4| 2526 (a) Graph the function. (b) Explain the shape of the graph by computing the limit as .r > ll\"r orasx > x. (c) Estimate the maximum and minimum values and then use calculus to nd the exact values. (d) Use a graph of f " to estimate the xcoordinates of the inection points. 25. 11X) = Jr\"' 26. IV) = (sinxyilu 2?. In Example 4 we considered a member of the family of functions r) = sin(.r + sin ex) that occur in PM synthesis. Here we investigate the function with c = 3. Start by graphing f in the viewing rectangle [[1, 71'] by [ 1.2, 1.2]. How many local maximum points do you see? The graph has more than are visible to the naked eye. To discover the hidden maximum and minimum points you will need to examine the graph of f' very carefully. In fact. it helps to look at the graph of f" at the same time. Find all the maximum and minimum values and inection points. Then graph f in the viewing rectangle [211. 211'] by [12, 1.2] and comment on symmetry. 2835 Describe how the graph of f varies as c varies. Graph several members of the family to illustrate the trends that you
