This quiz tests the work covered in Lecture 8 and corresponds to Section 2.2 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 probably wait until the end of lecture 9 before you attempt
it.

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, Chapter 2 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

$x\phantom{\rule{1em}{0ex}}$ | 1 | 1.5 | 2 | 2.5 | 3 |

$lnx\phantom{\rule{1em}{0ex}}$ | 0 | 0.4055 | 0.6931 | 0.9163 | 1.0986 |

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is correct!*

$x\phantom{\rule{1em}{0ex}}$ | 1 | 1.5 | 2 | 2.5 | 3 |

$lnx\phantom{\rule{1em}{0ex}}$ | 0 | 0.4055 | 0.6931 | 0.9163 | 1.0986 |

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is correct!*

*Choice (d) is incorrect*

Which of the following statements are 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.

*There is at least one mistake.*

For example, choice (e) should be False.

*There is at least one mistake.*

For example, choice (f) should be True.

*Correct!*

*False*Try again, the function is zero at B and G.*True*There is a turning point at D so the derivative is zero there.*True*The function has negative slope at both E and F and seems to be of about the same steepness. So the derivative is about the same at E and F.*False*The function has the same value at C and E but the derivative is positive at C and negative at E.*False*The function is negative at A but the derivative is positive.*True*The function crosses the $x$-axis at B and G and is therefore zero at those points.

Which of the following statements are correct? Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is correct!*

The gradient of the function is negative and much less steep at $x=4$ so

${f}^{\prime}\left(1\right)<{f}^{\prime}\left(4\right)\phantom{\rule{0.3em}{0ex}}.$

*Choice (c) is incorrect*

*Choice (d) is incorrect*