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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
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c) y=xé(l-3x2—x)4 3 d) y=[::;;]
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(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
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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
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Application '
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1. Determine the equation of the normal line to y: x 1 atx=-2. (5 nigrks) ‘j ' W
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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
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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»
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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 ,, ..
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”Sine ~4. ' [6] 2. Given f(x) =x2 +x+1 , g(x) =14- and hm = g(f(x)). Find h’(—2).
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[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.
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