Calculus Cumulative Test # 2 - Version 4
Name:
forsomecsuchthata<c<b. Whichof thefollowingcouldbetrue?
1./is continuous
for rr< x<b butnotdifferentiable
(e)
(C) Thegraphoflhas a cuspat x: c.
(A) x: c is a verticalasymptote
+ "f (r)
1T:/(r)
(E) None of the above
(D) flc) is undefined
2. If x3 +2xzy -4y= 7 , thenwhen' x : at, 4 x =
(c)-8
(D) -3
(E) 3.s
(A) -4.s
(B) 0
3. Letf andg be differentiablefunctionswith the following properties:
II. g(5)=2
L f(x)<0 forallx
'l',),
f
then g(x) =
If ft(x) = I9- and ft'(x) =
s@)
s@).
1
(A) + '(x).
f
(c) - "f(x)
(B) "f(x)
(D) 0
(E) 2
rateof changeat x:3 of the function/givenby /(x) =#,
4. Whatis theinstantaneous
(A)#
(c)*
(B)+
rn)i*
(E)+*
[ h 3 x . o < r -<3
5. If f(x)=.{*^"*
.then lim f(x)' is
x-+3l\ x l n 3-. 3 < x < 4 '
(A) ln9
(C) 3ln3
(B) ln27
(D) 3+ln3
(E) D.N.I'.
6. A particlemovesalongthex-axissothatits positionat time / is givenby x(r) = t2 -7t +12 . Forwhatvalueof r is the
velocityofthe particle zero?
(A) 2.s
(c) 3.5
(B) 3
(D) 4
(E)4.s
7. The graph of/has a horizontaltangentat the point (- 1, * 3), ajump at x: 0, and a cusp at (2,0). For what valuesofx is/
not differentiable.
(E)-1,2
(D)-1,0,and2
(C)-land0
(A)0
(B)0and2
8. An equationof the line tangentto the graph of y = 3x-cosx at x: 0 is
(C)y=3x+l
(B) y=2x-l
(A) y=2x
(D) v=3x-l
(E) v=4x
9. The minimumaccelerationattainedon the interval 0 < t 3 4 by the particlewhosevelocity is givenby
-4t2 -3t+2 is
v(t1=73
(A)-16
(B)-l0
(c)-8
-)5
(E)-3
(D)f
10. The function/is continuous on the closed interval [1, 3] and hbs the values given in the table. The equation f (r) =5
4
must have at least two solutions in the interval [1, 3] if k:
J
I
2
X
(x)
4
2
k
f
(A)
+
(B)1.s
I l. If /(x) = tan3x , tir"n "7'[fl
(c)2
(D)
?
(c) 6
(D) 616
(E)3
:
Iei
(A) 1
a
J
(B) 4
(E) 12
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f (4)
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I
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gJ'
_
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