 ## MATH1111 Quizzes

The Derivative Function Quiz
Web resources available Questions

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 Learning Hub (Mathematics) 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

Which of the following is the derivative of  $f\left(x\right)=3x+2\phantom{\rule{0.3em}{0ex}}?$ Exactly one option must be correct)
 a) ${f}^{\prime }\left(x\right)=2\phantom{\rule{0.3em}{0ex}}.$ b) ${f}^{\prime }\left(x\right)=3\phantom{\rule{0.3em}{0ex}}.$ c) ${f}^{\prime }\left(x\right)=5\phantom{\rule{0.3em}{0ex}}.$ d) There is not enough information to answer the question.

Choice (a) is incorrect
Try again, if $f\left(x\right)=mx+b$ then the derivative is $m\phantom{\rule{0.3em}{0ex}}.$
Choice (b) is correct!
Since the derivative of $f\left(x\right)=mx+b$ is $m\phantom{\rule{0.3em}{0ex}},\phantom{\rule{1em}{0ex}}{f}^{\prime }\left(x\right)=3\phantom{\rule{0.3em}{0ex}}.$
Choice (c) is incorrect
Try again, if $f\left(x\right)=mx+b$ then the derivative is $m\phantom{\rule{0.3em}{0ex}}.$
Choice (d) is incorrect
Try again, if $f\left(x\right)=mx+b$ then the derivative is $m\phantom{\rule{0.3em}{0ex}}.$
Which of the following graphs of $y=f\left(x\right)$ satisfy the following three conditions:
• ${f}^{\prime }\left(x\right)<0$ for $x<-1$
• ${f}^{\prime }\left(x\right)>0$ for $-1
• ${f}^{\prime }\left(x\right)=0$ for $x>2\phantom{\rule{0.3em}{0ex}}.$
Exactly one option must be correct)
 a) b) c) d) Choice (a) is correct!
Choice (b) is incorrect
Try again, thisgraph is of a function that is negative, positive and zero in the required region, not of a function whose derivative satisfies these conditions.
Choice (c) is incorrect
Try again, your graph has thewrong sign for its derivative.
Choice (d) is incorrect
Try again, you may need to review what having positive or negative derivativemeans.
Consider the graph below. Which of the following is the matching derivative function? Exactly one option must be correct)
 a) b) c) d) Choice (a) is correct!
The graph has turning points at$x=1$ and $x=3$ so the graph of the derivative must cut the axis at these points. The graph moves from positive gradient to negative gradient and back to positive so the graph of the derivative is positive then negative and then positive again.
Choice (b) is incorrect
Try again, this graph has thecorrect zeros but is not positive where the graph has positive gradient etc.
Choice (c) is incorrect
Try again, you do not have the zeros in the correct spots.
Choice (d) is incorrect
Try again, this graphdoes not have the correct zeros and is not positive where the graph has positive gradient etc.
Which of the statements below correctly match the function with its derivative?      Exactly one option must be correct)
 a) C is the graph of the derivative of BF is the graph of the derivative of CD is the graph of the derivative of AE is the graph of the derivative of D b) A is the graph of the derivative of CC is the graph of the derivative of FB is the graph of the derivative of DD is the graph of the derivative of E c) C is the graph of the derivative of AE is the graph of the derivative of CD is the graph of the derivative of BF is the graph of the derivative of D d) C is the graph of the derivative of AF is the graph of the derivative of CD is the graph of the derivative of BE is the graph of the derivative of D

Choice (a) is incorrect
Try again, looking carefully at the gradients of graphs A and B before the first turning point.
Choice (b) is incorrect
Try again, graph A represents a function with two turning points so its derivative must have 2 zeros. Look at the graphs again.
Choice (c) is incorrect
Try again, graph C has negative gradient and then positive gradient so its derivative cannot be graph E.
Choice (d) is correct!
Graph A has positive gradient to almost 1 and negative gradient to a bit more than 3 and then positive gradient. This matches graph C.
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.