**Firstly; there will be no MS 2001 lecture on Monday 6 December at 3 p.m. Instead you will have an MS 2003 lecture at this time in WG G 08. The 12 p.m. MS 2003 lecture on Wednesday December 1 in WG G 08 will now be an MS 2001 lecture. Indeed it will be the final MS 2001 lecture as Wednesday 8 December is a test day and the week after is review week. ****The morning lecture at 9 a.m. on Wednesday 1 December will still go ahead.**

*Second Derivative Test*and the

*First Derivative Test*. We showed that the First Derivative Test is superior as it can correctly handle all of the functions that the Second Derivative Test can and more (functions with vanishing second derivative and also functions that have points that are not differentiable).

*concave up*or

*concave down.*We defined a

*point of inflection*to be a point on the graph of a function where the concavity changes. We then said that we had a lot of tools that we could use to help sketch the graph of a function, and the final one we would examine would be

*asymptotes*. We introduced the

*horizontal asymptote*.

**Problems**

*You need to do exercises – all of the following you should be able to attempt. Do as many as you can/ want in the following order of most beneficial:*

*Wills’ Exercise Sheets*

Q. 10 from http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise4.pdf

*Other Exercise Sheets – ***Questions on the Second Derivative Test and Asymptotes**

Section 4 Q. 4-5 from Problems

*Past Exam Papers*

**Stationary Points are points where the derivative of a differentiable function , . **

**When asked to find the critical points of a function defined on the entire real line (rather than just on a closed interval ), the ‘endpoints’, are not considered critical points.**

**Convex is concave up and concave is concave down.**

Q. 5 from http://booleweb.ucc.ie/ExamPapers/exams2010/MathsStds/MS2001Sum2010.pdf

Q . 5 from http://booleweb.ucc.ie/ExamPapers/exams2009/MathsStds/MS2001s09.pdf

Q. 5 from http://booleweb.ucc.ie/ExamPapers/exams2009/MathsStds/Autumn/MS2001A09.pdf

Q. 5 from http://booleweb.ucc.ie/ExamPapers/exams2008/Maths_Stds/MS2001Sum08.pdf

Q. 3(b), 5 from http://booleweb.ucc.ie/ExamPapers/Exams2008/MathsStds/MS2001a08.pdf

Q. 5 from http://booleweb.ucc.ie/ExamPapers/exams2007/Maths_Stds/MS2001Sum2007.pdf

Q. 5(b), from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/MS2001Sum06.pdf

Q. 4(a), 5(b) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/Autumn/ms2001Aut.pdf

Q. 4(b),5(b), 6(a) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001.pdf

Q. 5(b), 6(a) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001Aut05.pdf

Q. 5(b) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/ms2001s2004.pdf

Q. 4(a), 5(b) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/MS2001aut.pdf

Q. 4(a), 5(b) from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/MS2001.pdf

Q. 5(b) from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/ms2001aut.pdf

Q. 5(b) from http://booleweb.ucc.ie/ExamPapers/exams2002/Maths_Stds/ms2001.pdf

Q. 4(a) from http://booleweb.ucc.ie/ExamPapers/exams2001/Maths_studies/MS2001Summer01.pdf

Q. 4(a), 6(a) from http://booleweb.ucc.ie/ExamPapers/exams/Mathematical_Studies/MS2001.pdf

*From the Class*

1. *Prove Theorem 5.2.2 (b)*

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