Calculus Questions assignment

Calculus Quiz
Hi,I need step by step solutions (can be typed or handwritten) for the questions in the attached file.Thanks

MATH 140
Sections 7380 (2208)
Fall 2020
Quiz #3
 The Quiz 3 is worth 100 points. There are 10 problems.
 This quiz is open book and open notes. This means that you may refer to your
textbook, notes, and online classroom materials, but you must work
independently and may not consult anyone (and confirm this with your
submission). You may take as much time as you wish, provided you turn in
your quiz no later than midnight, Tuesday, November 24, Eastern DaylightSaving Time (11:59 pm).
 Show work/explanation. Answers without any work may earn little, if any,
credit. You may type or write your work in your copy of the quiz, or if you
prefer, create a document containing your work. Scanned work is acceptable
also. Please try to have an organized, readable quiz.
 In your document, be sure to include your name and the assertion of
independence of work.
 General exam tips and instructions for submitting work are posted in the
Quizzes module.
Per the direction of the Dean’s Office, you are requested to include a brief note
at the beginning of your submitted exam, confirming that your work is your
“By typing my signature below, I pledge that this is my own work done in
accordance with the UMUC Policy 150.25 – Academic Dishonesty and
Plagiarism ( on
academic dishonesty and plagiarism. I have not received or given any
unauthorized assistance on this assignment/examination”. Signature (Your
Your submitted exam will be accepted only if you have included this statement.
If you have any questions, please contact me by e-mail.
1. In problems a-e you are given f ‘. Find a function f with the given derivative.
a. f ‘(x) = 4x + 2 b. f ‘(x) = 5ex c. f ‘(x) = 3sin2 x ∙cos(x)
d. f ‘(x) = 5(1+ex)4 ex e. f ‘(x) = ex+¿ sin(x)
2.The percent of a population, p(t), who have heard a rumor by time t is often
modeled p(t)= 100
1+ A et
=100¿for some positive constant A. Calculate how fast the
rumor is spreading dp(t)
dt .
3. For the parametric graph in Fig. 9, determine whether dx/dt, dy/dt, and dy/dx
are positive, negative or zero when t=1 and t=3.
4. A six-foot-tall person is walking away from a 14-foot-tall lamp post at 3 feet
per second (Fig. 16). When the person is 20 feet from the lamp post,
(a) How fast is the length of the person’s shadow changing?
(b) How fast is the tip of the shadow moving away from the lamp post? (Section
5. The length of a 12 foot by 8 foot rectangle is increasing at a rate of 3 feet per
second and the width is decreasing at 2 feet per second (Fig. 11).
(a) How fast is the perimeter changing?
(b) How fast is the area changing?
6. Find the derivative of x2 y3+4 xy=2 xusing theimplicit differentiation .
7. Find the equation of the tangent line when x=4 for the curve y+√x
= 3
8. The revenue function for a company is 60x – 0.5x2 and its cost function is
C(x) = 8x+12, where x is the daily production. If the daily production is
currently 20 units and the rate of change of production is 6 units per day, find
the rate at which the company’s profit is changing.
9. Determine where A(t) = t 2e(5−t) is increasing and decreasing.
10. Determine where in the interval [−1,20] the
function f(x)=ln(x44+20x3+100) is increasing and decreasing.

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