ex. 2.yBCO116 ELEMENTARY CALCULUS Task brief & rubrics Portfolio of Exercises 2

Task

Students are required to develop an individual report addressing the specific tasks set out in the guideline below.

Task briefing:

EXERCISE 1: Calculate the first derivative of the following functions and say the rule used in each case (25 points, 5 points each)

a)

b)

c) = 3 5 · sin ( )

d) = 4 4 +

4

+ 4 + √x + 4

e)

EXERCISE 2:

Given the following function: = −

+

a) Find the extreme points, and prove which ones of them are MAXIMA and MINIMA (15 points)

b) Find the inflection points of the function (10 points)

c) Draw the graph of the function (10 points)

EXERCISE 3:

Suppose that the revenues function of a certain product in function of the thousands of units sold yearly (x) is: R(x) = 5×2 -15x + 8

And the function of costs is: C(x) = x3 – 20×2 + 12x -1

a) What is the function of profits? (10 points)

b) Is there a production level that maximizes profit? If so, what are the points of maximum profit? (10 points)

c) What should be the sales that give the largest yearly revenue? (10 points)

d) What should be the sales that give the minimum yearly cost? (10 points)

=

Formalities:

• Word document.

• Wordcount: 500 words.

• Cover, Table of Contents, References and Appendix are excluded of the total wordcount.

• Font: Arial 12,5 pts.

• Text alignment: Justified.

• The in-text References and the Bibliography have to be in Harvard’s citation style.

Submission:

Week 2 – Via Moodle (Turnitin).

Deadline: 22nd November 2020 at 23:59 CEST.

Weight: This task is a 33% of your total grade for this subject.

It assesses the following learning outcomes.

On successful completion of this course, students will be able to:

– Interpret the derivatives of functions.

– Describe the notions of differentiability to algebraic functions.

– Understand and locate the concepts of derivatives within the business context to illustrate problems involving functions and interpret the results in that

context.

Rubrics.

Question Weight Criteria Grade Boundaries

(points per question)

1 25% If the student demonstrates excellent understanding of key concepts

and uses derivative methods in an entirely appropriate manner.

15

If the student computes the correct result 10

2 35% If the student demonstrates excellent understanding of key concepts

and uses derivative methods in an entirely appropriate manner.

20

If the student computes the correct result 15

3 40% If the student uses the right formulas 10

If the student demonstrates excellent understanding of key concepts

and uses derivative methods in an entirely appropriate manner.

20

If the student computes the correct result 10

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