Question

1. (30 pts.) Given that. (.r) = Determine 22-1 (a) The domain and intercepts of f. (b) Asymptotes off. (c) The intervals where f is increasing and where f is decreasing, (d) Local minimum and maximum values off. (e) Intervals where f is concave up and where f is concave down, (S) Inflection point off, (9) Sketch the graph of f. (You have to show all steps clearly otherwise you won't be awarded any credit)

Answer 1

Calculus Given 23 fix) x²_1 floy ý not defined when 2c²-1=0 = !! domain : (درا )v(ارا- بازار ته - ) DY IR - {11} (IRy real quů } Asymptote vertical x= Asymptote when os floe) to NO pc =-) are vertical Asymprote Horizontal Asympote oblique. asymbole fpx 19-21) oblique fly mpha-la 903 - -2 for OC²_1 . с - 32² (x²-1) x3 x 2x (2²-12 3764-3721 - 224 (QC2_1) 2 x43x² = 0 = x*(x+3)=0 (22-12 da + X=0, x= 3=0 Apco Plass and en are critical points

fix) = de ar + 09 on #ts) Yһске ацея feal decreally on (-6, -53) u (-13,0) (-53,-1) U (609 110 110 (13- *"*1 = 27thim since then 2) 2-0 O 50,4=0 (0,0) & intection 2 f"(0) - - point f"(13) 2013)2+ 6.13 39?-1)3 613 x2 1212 (3-1)3 E93 > 0 {"(-33) = 21-53)+6x=F3 :-1219 ((133-1) 3 -91920 free) = 313 and P") >0 (, 313 ŷ local minima Pix at x=13 ? then 2 at x= -13 fix) -313 and flors) to at x = -13 local maki ma 373

زهرا ) ا ( مرا-) on " (1) 20 اما) و (ه را-) frales con cave supon (ارہ) ں (ا-ره- ) on (x) 75 * concome down ů وx+ > (اره ما (1- ر - زهر 20 % Inflection point 0= (2) ال =0 at له

10 8 6 4 2 2 4 6 -2 -4 -6
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