MATH
Unit 2 Test Solutions (2) (1) (1)

Unit 2 Test Solutions (2) (1) (1) - yxi HW[2131qu MQV4U...

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Unformatted text preview: y‘xi: HW’“! [2131qu MQV4U TEST #2 - DERIVATIVES NAME: 5 (in? Knowledge = l% Application = ’ 6.. , Thinking = T Communication = . Communication = Knowledge 1. Differentiate each of the following. Do not simplify the derivative but you may rearrange the function before differentiating. (11 marks) a) y=4x8—3x+20 b) y=‘/(3x2—5x+7)3 L, '7 ‘2 a -3 WM) 1; . 1., 35—3 .2 iéaxhﬂﬂ) (b 3' c) y=xé(l-3x2—x)4 3 d) y=[::;;] I, '4 " ‘j -(glf(i“'}¢gxl~4¥) 4-3/[40‘33‘5’3 (”LIVE j'zsquvl.q<qawc’3'3.€uy 3 315+“ (3%+Q)2ﬂl : 5 W ”(L 3Y+ cum)" , 6 3 d)y= 5 +27:3 e)y=§i%54LT—l x x x J! E) :5x’i+.ﬂVS‘ UZSML’DN +2? -2; * 4)" 3L ’5 :7‘1‘15x a. v" “9X *1 5X A: (sway-(3‘51“?) 2. Find the slope of the tangent line to the curve y = (3x2 — 2)2\/ x2 ~ 5 and express your answer in simpliﬁed (factored) form. (4 marks) 3': 33%;) (we (BE/53:4— (muab‘ ié’f‘vﬁl .. L g 73- awaited; Links)? 4— 3L (53,3245 C3! “5) -L . ‘3 161:»:va Cocks") "‘ i much?) r (wk-13S “\$1“ . ' L v 1““, ‘ Unclear-190%?) (use, -bo «max l , «- weir“ : 2 (who) brim?) “(‘Sxih‘b‘g- ’3‘. y .l 2 e” 3 wew¢“* 3. , Find the points on the curve y = x3 -— x2 — x +1 where the tangent to the curve is horizontal. (4 marks) :13: Eli-«3.); v\/ 3:43- .. 2.31 .4 ‘90 . w ~no 3,£(;;--1‘)+! 0‘ D0 (x~n€&¥t“*k rel )1}? J Application ' 2_ a. , :i e 1. Determine the equation of the normal line to y: x 1 atx=-2. (5 nigrks) ‘j ' W . a. , 5x 2. . :2""i3(+‘5 3 ‘v. 4W 5 ,ﬂ Lil“ j / v a, 2w y ”I 7:; 51wa k / onL—S‘hL-t—S' ’C ("3’3 3,9 ’% ”Ti-\$5 _. l 1 43’1" _, j; :2 ' 3,0 4 #3 “\$2 :5 1., {£315— v ”:6 ‘Q «1512” km? ”4 / i; ,_ ’9 , “L I) . —» [O / 1“: ELK—L ‘ - q) 4. 9.1 if)? ‘ ' ‘3" C 1c”) The gas tank of a parked pickup truck develops a leak. The amount, V, in litres, of gas remaining in the 2 tank after t hours can be modelled by the function V(t) = 90(1— i) , 0 S t S 18 . 1 8 (a) How much gas was in the tank when the leak developed? (2 marks) VL‘E): 4°('~ (333' avian / (b) How fast is the gas leaking from the tank when there are 40L of gas in the tank? (4 marks) to (u: 12:; w V’H'B‘e “00%) («t-a) :3 i: x 0 (”5% at,“ at wt): _ll)~% Liv “3/ a i"% 3% :—\DL\~% ,- 16“,!" “t, ”m w}, V'le)="*°@“% ”Ta "" 3 3 "‘00“? / a: \$4»; 1’” %l 3. a For what values of x does the curve y = ~38 + 6x2 have its tangent line perpendicular to x-12y+5=0&£k:>/> ”“3“”; 3» jE—BL‘LA-DDC/ « - h" ‘ -33L7'M‘ML: ~49. .3 (:M) /., (32’? 35; Hi lb Li ,. x/W “”03 am; _ ’0‘ U :. “if m 1 50., Thinking 1. Find the points on the curve where the tangent lines to the parabola y: x2 +x passes through the point 1’ (2, 3). C9 (x) 3114303 W ,, .. " 11H /m 1 “6+3 W’“; V) K” i m: - m: XV)» a: 9.51»; 3:\’“l 317'+:r+3 Kai? . :50 / J/ 0)\ .4?! 31:4:xk3 3' (ﬁdbp’x ) _ 1— ,— , yHAHvS '11 ’9" 2' ./ 3/9/32 +3 74‘4“ 54*3'3‘7 —17-+»nc,+5 30/ 12-»wa “fa ‘9 a e; _s)m£§;= 6* / ”Sine ~4. ' [6] 2. Given f(x) =x2 +x+1 , g(x) =14- and hm = g(f(x)). Find h’(—2). x N0 9%ch ' */ n. .3”; Cwa‘X“ My)“; (11+xei3q [3] \ k m- mqu1+3z+hg®1+€5 WHEY?“ M— Lq ~1+| 5 Communication 1. Findd~y at x=8 if y=“+3 dx 2. Determine the values of a and b for the f’(~1)= 21. %g¥qh¥b~bﬂ0“ l‘BOwF‘vKE-wHD‘S \ mifion ﬁx) = (0:3 + bx2 + 3x — 6 , given that f(2) = 10 and .. Vl\\£' l):\ > {out N" 3““ >1. “" 3 .7 I. \gobb-BL-PJA) (”’13 *3 “*J" ...
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