dy 1. If fx ( ) is continuous at x = 3, then 13. If y x ) for x 0, then f (g(x)) = g (f (x)) when x = a. ½ b. ½ c. 1 b. 4x a. 3 b. 3 c.

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Gervais Simpson
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1 AP CALCULUS BC SUMMER ASSIGNMENT DO NOT SHOW YOUR WORK ON THIS! Complt ts problms during t last two wks of August. SHOW ALL WORK. Know ow to do ALL of ts problms, so do tm wll. Itms markd wit a * dnot tat a graping calculator may b us You will b tstd on Calculus A matrial (drivativs; C. -) witin t first fw wks of scool. You must do wll to continu in t cours 9 7. If f () and g( ) tn ( dy. If f ( ) continuous at, tn. If y ) for 0, tn f (g()) g (f ()) wn d f ( ) ½ ½ ( ) 0 0 ln ( ) ( ln ) 6 6 k 8. If t grap of f( ) as a point of ( ) ln sin. If f(), ow many zros dos f' inflction at, tn t valu of k. If, for all valus of, f' 0 and f'' 0 av on t closd intrval [0, ]? wic on of t following curvs could b a 0 part of t grap of f? 9. T grap of y symmtric wit lim T grap of wic function as y as an asymptot? y y y ln( + ) y y. If f( ) sin, tn f (0) 0 6. T quation of t tangnt lin to t curv y 69 at t point (, ) y 0 y 9 y 69 + y 0 + y 69 rspct to wic of t following? I T a II T y a III T origin I only II only III only II and III only I, II, and III d ln 0. ( ) d ln ln. For wat valus of t grap of y concav downward? No valus of < > < >. A particl movs along t a in suc a way tat its position at tim t givn by t t ( ). t Wat t acclration of t particl at tim t 0?. T maimum valu of f( ) 9 on [, ] 0 6. *T lim 69 nontnt 7. *Lt f and g b diffrntiabl functions suc f, g, f ' tat f g g If f g, tn ' ', ', '. 9 0

2 8. *T sortst dtanc from t curv y to t origin f( ) f() 9. *If f( ) 8, tn lim *How many ral solutions dos t quation sin(6 ) av? Non On Si Eigt Infinitly many. *If f( ) ( )( ), ow many numbrs in t intrval satfy t conclusion of t Man Valu Torm? Non On Two Tr Four. *If f '( ) sin tn f () may b cos cos cos cos cos. If f( ) ( ), tn t t drivativ of f 0! ()!( )!(+)!( ). At wat valu(s) of dos f( ) 8 av a rlativ minimum? 0 and only 0 and only 0 only and only, 0, and. T lim at 0 0 nontnt 6. Lt f b t function givn by f( ). Wat ar all valus of c tat satfy t conclusion of t Man Valu Torm on t closd intrval [,]? 0 only only only and and dy 7. If y y, tn d y + y y y 8. If g () ln(ln), tn g () ln (ln ) ln ln(ln ) y ln 9. If f ( ) for tn t rang of f All ral y y numbrs y y < 0. In wic intrval t function f( ) 6 9 incrasing? (, ) only (, ) only (,) only (, ) (,) (, ) (,). Wic of t following graps rprsnts an vn function?. For <, t drivativ of yln ( ). If f( ), tn f '(ln) sin, 0. Considr t function f ( ). In k, 0 ordr for f () to b continuous at 0 t valu of k must b 0 A numbr gratr tan. Wat ar all valus of for wic t grap of y 6 concav downward? 0 < < > < < 0 >

3 dy 6. If, tn y could b d 7. If t fundamntal priod of t function k f ( ) cos, tn k may b 6 8 n dy 8. If y, tn n d n ( n) n ( n ) 9. A particl movs on t a in suc a way tat its position at tim t givn by t t t 60t. For wat valus of t t particl moving to t lft? t only t and t t and t t only t, t, and t 0. T quation of t normal lin to t curv y y + 8 y 0 y + y + 8 y at t point wr f( ) f( a). *f a function suc tat lim 0. a a Wic of t following must b tru? lim f ( ) dos not t a f (a) dos not t f (a) 0 f (a) 0 f () continuous at 0. *If f( ) ( ), tn f '( ) 6 ( ). *Of t coics givn, wic valu NOT in t domain of t function f( ) (cos )?. *If f a function wic vrywr incrasing and concav upwards, wic statmnt tru about f,t invrs of f? f not a function. f f f f incrasing and concav upwards incrasing and concav downwards dcrasing and concav upwards dcrasing and concav downwards. *A function wos drivativ a constant multipl of itslf must b Priodic Linar Eponntial Quadratic Logaritmic 6. *For ow many ral numbrs it tru tat sin? 0 Tr Fiv Si Svn Infinitly many 7. *Wat t 0 t drivativ of cos? cos cos sin sin 0 8. *Suppos tat f a continuous function dfind for all ral numbrs and f ( ) and f ( ). If f () 0 for on and only on valu of tn wic of t following could b? T grap sows t dtanc st from a rfrnc point of a particl moving on a numbr lin, as a function of tim Wic of t points markd t closst to t point wr t acclration first bcoms ngativ? A B C A B C D E 0. *T function f ( ) tan( ) as on zro in t intrval [0,.]. T drivativ at t point undfind sin. T lim 0 nontnt. If y, tn y as a point of inflction at 0 D E

4 . If t radius of a spr incrasing at t rat of incs pr scond, ow fast, in cubic incs pr scond, t volum incrasing wn t radius 0 incs? Wat ar all valus of for wic ln( ) 0? > ( ). T lim ( ) 0 nontnt 6. If f () ln and g( ), tn f (g()) ln 7. If f ( ) arctan, tn ' f 8. If f () cos(arcsin), wat t rang of f? { 0} { } { 0 } { } { 0 } 9. Wic of t following tru about t grap of y? It asymptotic to t -a. It as a rlativ maimum at 0. It always concav upwar It dcrasing for all gratr tan 0. It as a point of inflction at If f tn f ' 0 6. T coordinats of t point on t curv y wic closst to (,) (,) (,) (,0),, 6. lim 6. A particl movs along t a so tat at any tim t its position givn by t t t. For wat valus of t t vlocity of t particl incrasing? t > only 0 < t < only < t < only t < or t > 0 < t < or t > 6. * T quations of t tangnt lin to t curv y 6 at its point of inflction y + 8 y + 0 y 8 y + y 0 g() g( ) 6. *If lim 0.68, tn at t point, t grap of g () dcrasing incrasing concav upwards concav downwards attains a rlativ minimum point 66. *For 0, an antidrivativ of tan ln(sc) sc ln(sc ) ln(cos) ln(sc) 67. * If t drivativ of a function f givn by f '( ) sin( ), tn ow many critical points dos t function f () av on t intrval [0.,.6]? *T drivativ of ( ) ( ) ( ) ( ) 7 ( ) ( ) ( ) ( ) 69. *T scond drivativ of a function givn by f ''( ) 0. cos. How many points of inflction dos t function f () av on t intrval 0 0? Non Tr Si Svn Tn 70. *T quation of t lin tangnt to t curv k 8 y k at y +. Wat t valu of k?

5 7. *How many zros dos t function y sin(ln) av for 0 <? On Two Tr Four Mor tan four 7. *For all f 0, if (ln ), tn f () ln ln 7. Wat t domain of t function f ( ) {: } {: } {: or > } {: > } {: < } 7. T position of a particl on t a at tim t, t > 0, lnt. T avrag vlocity of t particl for t fn ( ) 7. If fn ( ) and f (), tn f (7) If f ( ), 0, and f (g ()), tn g () ( ) ( + ) 77. T slop of t lin normal to t grap of yln at ½ undfind 78. T minimum valu of f( ) ln ( ln) 79. If f () +, tn f () nontnt 80. T volum of an panding spr incrasing at a rat of cubic ft pr scon Wn t volum of t spr 6 cubic ft, ow fast, in squar ft pr scond, t surfac ara incrasing? ( ) dy 8. If y, tn d ( ) ( ) ( ) (ln) ( ) ( ) ( ) (ln) ( ) (ln) dy 8. If y, tn d 0 ( ) 8. T fundamntal priod for t grap of ysin ( ) d sin 8. d cos cos cot cos ( cos ) cos cos( ) cos( ) 8. T lim 0 0 dy 86. If y arcsin, tn d If t grap of a function f symmtric about t y-a, and contains t point (,), wic point also on f? (, ) (, ) (0,0) (,) (,) y 88. *If, tn at t point (,ln), dy d ln ln ln ln 89. *At t point of intrsction of f () cos and g( ), t tangnt lins ar t sam lin paralll lins prpndicular lins intrscting but not prpndicular lins non of t abov

6 tan( ) tan( ) 90. *T lim 0 0 cot() sc ( ) nontnt sc ( ) 9. *A particl movs along t -a so tat its position at any tim t > 0 givn by ( t) t 0t 9t 6t. For wic valu of t t spd t gratst? t t t t t 9. *A particl movs along t -a so tat at any tim t its position givn by ( t) sint cos( t). Wat t acclration of t particl at t? *T drivativ of a function if givn by f '( ) (sin )(cos ( )). Wic of t following tru about t function f( ) for? f () an odd function f () incrasing for all valus in t intrval f () as actly on rlativ minimum in t intrval f () as no points of inflction in t intrval f ( ) t absolut minimum valu 9. *How many points of inflction dos t 8 function f ( ) av? Non On Two Tr Infinitly many 9. *T function y b 8 as a orizontal tangnt and a point of inflction for t sam valu of. Wat must b t valu of b? If y ( ), tn dy d 6 ( ) ( ) 6( ) 6 ( ) 97. If t grap of a function f as a orizontal tangnt at t point (,), wat t quation of t normal lin at t point? y y y If f( ) and if c t only ral numbr suc tat f (c) 0, tn c btwn and and 0 0 and and and 99. T grap of y 8 Incrasing for all Dcrasing for all Only dcrasing for all suc tat > Only incrasing for all suc tat < Only dcrasing for all suc tat < 00. For ow many ral numbrs dos ln? 0 Infinitly many 0. If f( ), tn f '( ) sin( y), tn dy d sc( y) sc y sc y y sc( y) y sc( y) y 0. How many points of inflction dos t grap 6 of y 9 0 av? Non On Two Tr Four 0. lim 0 ½ ln nontnt 0. T grap of y as No orizontal asymptots and on vrtical asymptot On orizontal asymptot and on vrtical asymptot Two orizontal asymptots and on vrtical asymptot On orizontal asymptot and two vrtical asymptots Two orizontal asymptots and two vrtical asymptots, 06. If f ( ), tn f (), ½ nontnt

7 8 k 07. For wat valu of k will av a rlativ minimum at? If f a function suc tat f (0), f (), fn ( ) and fn ( ) for all intgrs n 0, wat fn ( ) t valu of f ()? 8 It cannot b dtrmind from t givn information givn. 09. Wat t maimum valu of t drivativ of f( )? 0 0. If f( ), wat t drivativ of t invrs of f ()? ( ) ( ). * lim *Wat t 0 t drivativ of y sin()? 0 0 sin( ) sin( ) 9 0 cos( ) cos( ) cos( ). *Suppos tat f () a twic-diffrntiabl function on t closd intrval [a,b]. If f (c) 0 for a < c < b, wic of t following statmnts must b tru? I. f (a) f (b) II. f as a rlativ trmum at c III. f as a point of inflction at c Non I only II only I and II II and III d. * ln d 0 ln ln ln. *Lt f b a function wic continuous on [,0] and wos drivativ givn by cos f'( ). Wic of t following tru ln( ) about f () on t intrval [,0]? I. f () monotonic II. f () as a rlativ minimum III. f () as tr points of inflction I only II only III only II and III only I, II, and III 6. *If f a continuous function on t closd intrval [a,b], wic of t following NOT ncssarily tru? I. f as a minimum on [a,b] II. f as a maimum on [a,b] III. f (c) 0 for a < c < b I only II only III only I and II only I, II, and III 7. *A particl movs along t -a so tat its position at any tim t > 0 givn by ( t) t t 6cos( t). For wat valu of t t vlocity ngativ? t ½ t t t T vlocity nvr ngativ 8. Wic of t following functions symmtric wit rspct to t origin? y y y y sin y cos ( ) 9. T lim 0 at t point If f( ) ( ) cos, tn f (0) 0. Wat t domain of t function f givn by f ( ) ln? {: < } {: } {: > } {: < < } {: < or > }. lim 0 nontnt. If t lin y + tangnt to t curv y c, tn c 7 sin. If f ( ), tn f () cos cos sin sin cos cos

8 . T quation of t orizontal asymptot for t grap of y y y ½ y y ½ y, 6. Lt f ( ). Wic of t following, statmnts corrct? f () continuous at sinc f () dfind at. f () continuous at sinc lim f ( ) ts. f () not continuous at sinc f () not dfind at. f () not continuous at sinc lim f ( ) dos not t. f () not continuous at sinc lim f( ) f(). 7. T quation of t tangnt lin to t curv y at t point (,7) y + y y 7 0 y + y 8 8. If yln( ), tn dy d 9 ( ) ( ) 9 ( ) ( ) 9. T drivativ of 0. If f( ) and g( ) t invrs function of f (), tn f (g(ln)) ¼ ½ ln ln. Wat t ara of t largst rctangl wit lowr bas on t a and uppr vrtics on t curv y? lim ln 9. If y y, tn dy at (, ) d 6 8 kln. *T maimum valu of occurs wn k k + k k + k. *How many trma (maimum and minimum) dos t function f( ) ( ) ( ) av on t intrval 6? Non On Two Tr Four 6. *T tangnt lin to t grap of y sin at t point, crosss t sin grap at t point wr *If f( ), tn t avrag rat of cang of f on t intrval [0,] *Wic statmnt tru for t function f () ln(tan) on t intrval? f () incrasing at an incrasing rat f () incrasing at a dcrasing rat f () as an absolut maimum in t opn intrval f () as a point of inflction in t opn intrval f () as a point of symmtry in t opn intrval 9. *A company must manufactur calculators wkly tat can b sold for dollars ac, at a cost of dollars for manufacturing calculators. T numbr of calculators t company sould manufactur wkly in ordr to maimiz its wkly profit *A msil rs vrtically from a point on t ground 7,000 ft from a radar station. If t msil ring at a rat of 6,00 ft pr minut at t instant wn it 8,000 ft ig, wat t rat of cang, in radians pr minut, of t msil s angl of lvation from t radar station at t instant?

AP Calculus Multiple-Choice Question Collection

AP Calculus Multiple-Choice Question Collection AP Calculus Multipl-Coic Qustion Collction 985 998 . f is a continuous function dfind for all ral numbrs and if t maimum valu of f () is 5 and t minimum valu of f () is 7, tn wic of t following must b