Bc12 Fall Final Mc

7/25/2019 Bc12 Fall Final Mc

1/14

BC 11-12

Fall Final Part I

No Calculator Allowed

1. An equation of the line tangent to the curve y =kx + 8

k+x atx=

!2 is y = x + 4

What is the value of k?

a) -3 b) -1 c) 1 d) 3 e) 4

2. Let f x( )be a continuous and differentiable function on the interval

0 < x


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4. The graph of a twice differentiable function f is shown below. Which of

the following is true?

(a)

(b)

(c)

(d)

(e)

5. If sin xy( ) = x2 , then dydx

=

(a) 2xsec xy( )

(b)

sec xy( )x

2

(c) 2xsec xy( )!y

(d)

2xsec xy( )y

(e)

2xsec xy( )!yx

7!

#


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6. The given functionfhas a removable discontinuity atx= -5. FindA.

f x( ) =

5x2 + 8, if x < !5

8x,

if

x =!5Ax + 8, if !5


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8. This problem involves finding the absolute maximum and absolute

minimum of the function f x( ) =x 3 ! 3x + 4 restricted to the closed interval

x! 0,

2"# $% . Which of the following statements is correct?

(a)

f x( ) has both an absolute maximum and absolute minimum at the end

points.

(b) f x( ) has both an absolute maximum and absolute minimum at interior

points.

(c) f x( ) has both an absolute maximum at an end point and an absolute

minimum at an interior point.

(d)

f x( ) has both an absolute maximum at an interior point and an absolute

minimum at an end point.

(e)

None of the above

9. Which of the following improper integrals converge?

I.

e!x

0

"

# dx II.1

x2

0

1!

"# dx III.

1

x0

1!

"# dx

(a) I only (b) III only (c) I and II only

(d) II and III only (e) I and III only

10. If f and gare continuously differentiable functions defined for all real

numbers, which of the following integrals would equal f g 4( )( )! f g 2( )( ) ?

a) f ' g x( )( )dx2

4

! b) f g x( )( )f' x( )dx24

! c) f g ' x( )( )g ' x( )dx24

!

d) f g x( )( )g ' x( )dx2

4

! e) f' g x( )( )g ' x( )dx24

!


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11. A particle is moving upward along the y-axis until it reaches the origin and

then it moves downward such that v t( ) =8 ! 2t for t! 0 . The position of the

particle at time t is given by

(a) y t( ) =!t2

+ 8t!16 (b) y t( ) =!t

2

+ 8t+16 (c) y t( ) =2t2 ! 8t!16 (d) y t( ) =8t! t2

(e) y t( ) =8t! 2t2

12.1

2

!"#

$%&

n=1

'

(2n

(a) 13

(b) 12

(c) 1 (d) 2 (e) !

13. limx!2

x2 " 4

cos #t( )dt2

x

$=

(a) 0 (b) 1 (c) 2 (d) 4 (e) DNE

14.x!x3

x2

dx1

e2

"

(a) 3! e2 (b) 3! e4 (c) 5! e2

(d) 5! e4 (e) DNE


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15. At which x-value isf(graphed above) continuous but not differentiable?

(a) 0 (b) 1 (c) 2 (d) 5 (e) nowhere

16. 6. The graph off, the derivative off,

is shown to the right. Which of the following

statements about the function are true?

I.

f is increasing on the interval !2,!1( ) .

II.

f has a minimum at x=1.

III. f is increasing on the interval !1,1( )

IV. fhas a minimum at x=!1.

(a) I and II (b) II and III (c) III and IV

(d) I and IV (e) I, II, and IV

f


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17. Iff andg are twice differentiable and if h(x) =g (f(x)), then h(x) =

(a)

g" f x( )( )

(b)

g" f x( )( )f" x( )

(c)

g" f x( )( ) f' x( )!" #$2

(d) g' f x( )( ) f' x( )!" #$2

+ f' x( )g" f x( )( )

(e)

g' f x( )( )f'' x( )+ f' x( )!" #$2

g" f x( )( )

18 The graph of f ' x( ) , the derivative of f , is shown below for !2 " x" 5 . On

what intervals is f increasing?

a) !2,1( ) only b) !2,1( ) and 1 !2,3( ) c) 3,5( )

d) 0,

1.5( )and 3,5( ) e) !2,!1( ) , 1,2( ) , and 4,5( )


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19. Which of the following differential equations corresponds to the slope field

shown in the figure below?

a)dy

dx =!

y

x b)

dy

dx =

1

5xy c)

dy

dx =

1

10xy

d)dy

dx =

y

x e)

dy

dx =

x

y

20. If f' x( ) =!4 x ! 6( )2

x ! 9( ) which of the following is true abouty=f(x)?

a) fhas a point of inflection atx= 6 and a local minimum atx= 9.

b) fhas a local maximum atx= 5 and a local minimum atx= 9.

c) fhas a local minimum atx= 6 and a local maximum atx= 9.

d) fhas a local minimum atx= 6 and a point of inflection atx= 9.

e) fhas a point of inflection atx= 6 and a local maximum atx= 9.


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BC 11-12

Fall Final Part II

Calculator Allowed

1.

2.


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3. The graph of the derivative offis shown below. Which of the following

must be true?

a) fhas a local minimum atx= -3.

b) fhas a local maximum atx= 0.

c) fis concave down on [0, 6].

d) fhas a point of inflection atx= 6.

e) fis increasing on [-3, 3].

4. At what point on the graph of f below is f' > 0

, and f" > 0

a) M b) N c) P d) Q e) R


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5.

6. If f x( ) = x2 !1 , which of the following is equal to f' 3( ) ?

(a) limx!3

x + h( )2

"1" 8

x " 3 (b) lim

h!0

x + h( )2

"1" x2"1

h

(c) limh!0

x + h( )2

"1" 8

h (d) lim

x!3

x2"1" 8

x " 3

(e) limh!0

x2"1" 8

x " 3

7. u!5

4 du1

"

#

(a) 4 (b)5

4 (c)

1

4 (d) -4 (e) DNE


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8.

9. At what point on the graph of y =1

2x2 is the tangent parallel to the line

2x ! 4y = 3

(a)1

2,! 1

2

"#$

%&'

(b)1

2,1

8

!"#

$%&

(c)1

2,!1

4

"#$

%&'

(d) 1,! 12

"#$

%&'

(e) 2,2( )


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10.

11.


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12. A particle moves along a straight line such that its position is given by

s = 4t3! 9t

2+ 6t+ 2 for t! 0 . When is the particle at rest?

(a) t=1

2 (b) t=1 (c) t= 0

(d) t= 0,1

2 (e) t=

1

2, 1

Bc12 Fall Final Mc

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