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MAT1339 C
Fall 2014
Assignment 2
Due: October 22
Instructor: Camelia Karimianpour
Instructions:
You should show your work for multiple choice questions.
For long questions you should write all the steps, similar to what we did in
class.
You can work in a group but you should write your own assignments. You
are not allowed to copy another student’s work. Note that plagiarism is taken
very seriously at the University of Ottawa.
This assignment is worth 5% of your final grade.
Question 1 (2 marks) Find the value of k such that x = 2 is a critical
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number of f (x) = x4 − 3x2 + kx.
4
1. 4
2.
5
2
3. 2
4. −2
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Question 2 (2 marks) Find the domain of the function f (x) = p
.
(x − 1)(x − 3)
1. (1, 3)
2. [1, 3]
S
3. (−∞, 1) (3, +∞)
4. (1, +∞)
√
√
Question 3 (2 marks) Find all the critical numbers of f (x) = 6 x − x x.
1. x = 0 and x = 1.
2. x = 0 and x = 3.
3. x = 1 and x = 3.
4. x = 0 and x = 2.
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Question 4 (8 marks) Let f (x) = 14 x4 − 2x2 + 5.
Find the absolute maximum value and minimum value of f (x) on [−4, 4].
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Question 5 (8 marks) We wish to design an open storage box ( no top)
with a square base. The storage box must have a volume of 16 cm3 . The
bottom costs $4 per square centimetre and the sides costs $1 per square
centimetre. Find the dimensions that will minimize the total cost. What
will the minimum cost be?
4
2
−4
.
Question 6 (18 marks) Let f (x) = xx2 −9
(a) (3 marks) State the domain, x-intercept(s) and y-intercept(s).
(b) (2 marks) Find all the possible horizontal and vertical asymptotes.
(c) (2 marks) Find f 0 (x) and f 00 (x).
(d) (4 marks) Find all the critical numbers, state all the intervals of
increase and decrease, find all the local minimum points and all the local
maximum points.
(e) (4 marks) Find all the points of inflection, and state intervals of concavity.
(f) (3 marks) Sketch the graph.
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Use this page if you need more space.
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