CALCULUS I
FINAL EXAM
Sample 4
Student Name: ___________________________________________
Student ID Number: ______________________________________
Course Title: Calculus I
Duration of Exam: 2 Hours
Number of Exam Pages: 9 pages (including this cover sheet)
Exam Type: Closed book
Additional Materials Allowed: Calculator and Formula sheet
Total Mark: /100
,Question 1 (3 marks)
Suppose that 𝑓(𝑥) is twice-differentiable function and that the graph of 𝑦 = 𝑓(𝑥) is shown below.
(a) Which of the following best describe the value of 𝑓 ′ (0) ?
A. It is positive.
B. It is negative.
C. It is zero.
D. Its sign cannot be determined from the graph.
(b) Which of the following best describe the value of 𝑓 ′′ (−3) ?
A. It is positive.
B. It is negative.
C. It is zero.
D. Its sign cannot be determined from the graph.
(c) How many inflection points does 𝑓 have in the interval [−3,2] ?
, Question 2 (8 marks)
Consider the function
2
𝑓(𝑥) = 𝑥 3 − 5𝑥 2 + 12𝑥.
3
(a) Find all intervals where 𝑓 is increasing.
(b) Find all intervals where 𝑓 is decreasing.
(c) Find all intervals where 𝑓 is concave up.
FINAL EXAM
Sample 4
Student Name: ___________________________________________
Student ID Number: ______________________________________
Course Title: Calculus I
Duration of Exam: 2 Hours
Number of Exam Pages: 9 pages (including this cover sheet)
Exam Type: Closed book
Additional Materials Allowed: Calculator and Formula sheet
Total Mark: /100
,Question 1 (3 marks)
Suppose that 𝑓(𝑥) is twice-differentiable function and that the graph of 𝑦 = 𝑓(𝑥) is shown below.
(a) Which of the following best describe the value of 𝑓 ′ (0) ?
A. It is positive.
B. It is negative.
C. It is zero.
D. Its sign cannot be determined from the graph.
(b) Which of the following best describe the value of 𝑓 ′′ (−3) ?
A. It is positive.
B. It is negative.
C. It is zero.
D. Its sign cannot be determined from the graph.
(c) How many inflection points does 𝑓 have in the interval [−3,2] ?
, Question 2 (8 marks)
Consider the function
2
𝑓(𝑥) = 𝑥 3 − 5𝑥 2 + 12𝑥.
3
(a) Find all intervals where 𝑓 is increasing.
(b) Find all intervals where 𝑓 is decreasing.
(c) Find all intervals where 𝑓 is concave up.
