© 2009  Rasmus ehf  & Jóhann Ísak Pétursson

Functions 2  Test 5

Instructions to students

  Read each question carefully and choose the answer that you think is most likely to be correct. You can only choose one answer for each question. When  you are ready, mark your answers in the spaces on the computer screen and click on the button 'Send answers'. Good luck!

 

1.                              Find the second derivative of  f(x) = x4 + x3 + x2 + x + 1

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Possible answers:
A f´´(x) = 12x2 + 6x
B f´´(x) = 12x2 + 6x + 2
C f´´(x) = 4x3 + 3x2 + 2x
D

f´´(x) = 4x3 + 3x2 + 2x + 1

2.                          Find the second derivative of f(x) = sin x + cos x

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Possible answers:
A f´´(x) = –sin x – cos x
B f´´(x) = –sin x + cos x
C f´´(x) = sin x – cos x
D

f´´(x) = sin x + cos x

3.                          Find the second derivative of f(x) = –cos ex

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Possible answers:
A f´´(x) = ex · sin ex
B f´´(x) = – ex · sin ex
C f´´(x) = 2·ex · sin ex
D f´´(x) = ex(sin ex + cos ex)

 

4.                             Find the second derivative of f(x) = ln(x2 + 1)

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Possible answers:
A f´´(x) = x2 + 1
B f´´(x) = –(x2 + 1)–2
C f´´(x) = (2 – 2x2)/(x2 + 1)2
D f´´(x) = (x2 + 1)·ln(2x/(x2 + 1)2)

 

5.                                    Find the point of inflexion if  f(x) = x3 – 6x2 + 6x + 6

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Possible answers:
A (0, 0)
B (1, 1)
C (2, 2)
D (3, 3)

6.                               Find the point of inflexion if f(x) = sin x for 0 < x < 2.

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Possible answers:
A (/4, 0)
B (, 0)
C (/2, 1)
D (3/2, –1)

7.           Find the interval on which the graph of  f(x) = x3 – x + 1 is convex ( bends upwards).

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Possible answers:
A –1 < x < 1
B x > 0
C x < 0
D in all the set  R

8.        Find the interval on which the graph of  f(x) = x4 – 6x2 + 6x – 6 is concave ( bends downwards).

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Possible answers:
A –1 < x < 1
B x > 0
C x < 0
D
in all the set  R

9.            Which of the following lines is a tangent  to f(x) = 3 – 9x + 6x2 – x3 in the point of inflexion?

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Possible answers:
A y = x – 1
B

y = 2x + 1
C y = 3x – 5
D y = 4x + 5

10.          Which of the following lines is a tangent to f(x) = 0.25x4 – 1.5x2 + 0.25 in the point of inflexion ?

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Possible answers:
A y = x – 1
B

y = 2x + 1
C y = 3x – 5
D y = 4x + 5

 

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