This quiz tests the work covered in Lecture 9 and corresponds to Section 2.3 of the
textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et
al.).

There is a web quiz at Wiley. It is the same quiz for each section in Chapter and you
should you attempt it now.

Be aware that it doesn’t seem to accept the written answers so you will have to check
whether your answers are correct when they print the correct answer. Questions 11
and 12 were illegible on 14/11/05.

The Mathematics Learning Centre has a booklet on differentiation Introduction to
Differential Calculus which covers all of the topics for the next few lectures. In
particular, Chapters 2 and 3.1 of the booklet covers this topic.

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 correct!*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

- ${f}^{\prime}\left(x\right)<0$ for $x<-1$
- ${f}^{\prime}\left(x\right)>0$ for $-1<x<2$
- ${f}^{\prime}\left(x\right)=0$ for $x>2\phantom{\rule{0.3em}{0ex}}.$

*Choice (a) is correct!*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

Which of the following is the matching derivative function? Exactly one option must be correct)

*Choice (a) is correct!*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is correct!*

Graph C has negative gradient to a bit more than 2 and then positive gradient. This matches graph F.

Similarly for the other 3 graphs.