This quiz tests the work covered in Lecture 10 and corresponds to Section 2.4 of the
textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et
al.).

I can’t find any sites appropriate for this topic but it would be worth going to the sites from the previous topic to consolidate what you have learned.

You should be able to attempt web quiz at Wiley.

The Learning Hub (Mathematics) booklet Introduction to Differential Calculus covers all of the topics for these lectures. In particular, Chapters 1 to 3.1 of the booklet cover the topics from Week 3.

The site http://www.math.uncc.edu/$\sim $bjwichno/fall2004-math1242-006/Review˙Calc˙I/lec˙deriv.htm
covers some of the material in Section 2.1-2.3

There is an applet that lets you sketch the derivative of a given function at http://www.ltcconline.net/greenl/java/Other/DerivativeGraph/classes/DerivativeGraph.html After you have mastered the topic you might like to try the tests at http://www.univie.ac.at/future.media/moe/tests/diff1/defabl.html and http://www.univie.ac.at/future.media/moe/tests/diff1/poldiff.html and the puzzle at http://www.univie.ac.at/future.media/moe/tests/diff1/ablerkennen.html

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is correct!*

There may be more than one correct answer. (Zero or more options can be correct)

*There is at least one mistake.*

For example, choice (a) should be False.

*There is at least one mistake.*

For example, choice (b) should be True.

*There is at least one mistake.*

For example, choice (c) should be True.

*There is at least one mistake.*

For example, choice (d) should be False.

Recall ${\left.\frac{dy}{dx}\right|}_{x=2}$ gives the value of the derivative at $x=2\phantom{\rule{0.3em}{0ex}}.$

*Correct!*

*False*Try again, ${\left.\frac{dy}{dx}\right|}_{x=2}$ gives the value of the derivative at $x=2\phantom{\rule{0.3em}{0ex}}.$*True*${\left.\frac{dy}{dx}\right|}_{x=2}$ gives the value of the derivative at $x=2\phantom{\rule{0.3em}{0ex}}.$*True*When the derivative is positive at a point the function is increasing.*False*Try again, we have no information about what is happening at $x=12\phantom{\rule{0.3em}{0ex}}.$

Recall ${\left.\frac{dy}{dx}\right|}_{x=2}$ gives the value of the derivative at $x=2\phantom{\rule{0.3em}{0ex}}.$

Newton’s law of cooling tells us that if the object is cooling then $\frac{dT}{dt}=-k\left(T-A\right)$ where $k$ is a constant of proportionality.

Which of the following gives the correct interpretation of $\frac{dT}{dt}\phantom{\rule{0.3em}{0ex}}?$ Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is correct!*

Newton’s law of cooling tells us that if the object is cooling then $\frac{dT}{dt}=-k\left(T-A\right)$ where $k$ is a constant of proportionality.

Which of the following describes the meaning of ${\left.\frac{dT}{dt}\right|}_{t=1}=-0.676\phantom{\rule{0.3em}{0ex}}?$ Exactly one option must be correct)

*Choice (a) is correct!*

So after 1 hour the object is losing approximately 0.676 degree of temperature per hour.

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*