Final Exam Calculus 1 with solution (Sample 4)

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.