Diagnostic Quiz 2: Some calculus

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Question 1

Find the value of the derivative f(1) for the following function: f(x) = x2 + 6x - 5
a)
8
  b)
3
c)
2
  d)
10 3
e)
- 3

 

Your answer is correct.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 2

Find the derivative of the following function: f(x) = cosx - sinx
a)
f(x) = sinx - cosx
  b)
f(x) = sinx + cosx
c)
f(x) = cosx - sinx
  d)
f(x) = -cosx - sinx
e)
f(x) = -1 - tanx

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
Not correct. Choice (e) is false.

Question 3

Find the derivative of the following function: f(x) = x
a)
f(x) = 2 x
  b)
f(x) = - 2 x
c)
f(x) = 1 2x
  d)
f(x) = - 1 2x
e)
f(x) = 2 3x32

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 4

Find the derivative of the following function: f(x) = e3x
a)
f(x) = e3x
  b)
f(x) = 3xe3x
c)
f(x) = e3x 3
  d)
f(x) = e3x + 3
e)
f(x) = 3e3x

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Your answer is correct.

Question 5

Find the derivative of the following function: f(x) = x2 lnx
a)
f(x) = x
  b)
f(x) = 2x + 1 x
c)
f(x) = 2x -1 x
  d)
f(x) = x(2lnx + 1)
e)
f(x) = 2xlnx + 1 x

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
Not correct. Choice (e) is false.

Question 6

Find the derivative of the following function: f(x) = x - 1 x2 + 1
a)
f(x) = 1 + 2x - x2 (x2 + 1)2
  b)
f(x) = 1 + 2x - x2 x2 + 1
c)
f(x) = (x + 1)2 x2 + 1
  d)
f(x) = (x - 1)2 x2 + 1
e)
f(x) = 1 - 2x - x2 (x2 + 1)2

 

Your answer is correct.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 7

Find the equation of the tangent line to the curve y = x3 - x + 4 at the point (-1,4).
a)
y = -4x
  b)
y = -x + 3
c)
y = x + 5
  d)
y = 2x + 6
e)
y = -2x + 2

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
Not correct. Choice (e) is false.

Question 8

Find the maximum value of f(x) = x3 - 3x2 - 9x + 2 for - 2 x 1.
a)
7
  b)
2
c)
- 9
  d)
0
e)
15 2

 

Your answer is correct.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 9

Evaluate the definite integral 12x2 + 5x - 1dx.
a)
23 6
  b)
53 6
c)
17 3
  d)
9
e)
55 6

 

Not correct. Choice (a) is false.
Your answer is correct.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 10

Find the indefinite integral sin2xdx.
a)
cos2x + C
  b)
- 2cos2x + C
c)
cos2x 2 + C
  d)
2cos2x + C
e)
-cos2x 2 + C

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Your answer is correct.
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