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MATH1011 Diagnostic Quizzes

Diagnostic Quiz 2: Some calculus
Question 1 Questions
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

Choice (a) is correct!
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is incorrect
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

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is correct!
Choice (e) is incorrect
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

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
Choice (d) is incorrect
Choice (e) is incorrect
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

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is correct!
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

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is correct!
Choice (e) is incorrect
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

Choice (a) is correct!
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is incorrect
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

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is correct!
Choice (e) is incorrect
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

Choice (a) is correct!
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is incorrect
Evaluate the definite integral 12x2 + 5x 1dx.
a)
23 6
 b)
53 6
c)
17 3
 d)
9
e)
55 6

Choice (a) is incorrect
Choice (b) is correct!
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is incorrect
Find the indefinite integral sin2xdx.
a)
cos2x + C
 b)
2cos2x + C
c)
cos2x 2 + C
 d)
2cos2x + C
e)
cos2x 2 + C

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is correct!