**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.**

*where*the functions were differentiable and what rule could be used to find the derivative where differentiable. We did Q. 4(i), Q. 10(i),(ii) and finally Q. 12. With a test in three weeks ye need to keep up the work on exercises.

**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*

Use the Closed Interval Method to do Q. 8 (i), (iii) from

http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise1.pdf

Q. 14-17 from http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise3.pdf

Q. 2 from http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise4.pdf

*Other Exercise Sheets*

Section 4 Q. 1-3 from Problems

*Past Exam Papers*

**Those questions in bold are to be done using the Closed Interval Method. ***Those questions in italic request the critical points of a function rather than . In these questions the ‘endpoints’ are not considered critical points.*

Q. **2(a)** from http://booleweb.ucc.ie/ExamPapers/exams2010/MathsStds/MS2001Sum2010.pdf

Q . **2**, 3(b) from http://booleweb.ucc.ie/ExamPapers/exams2009/MathsStds/MS2001s09.pdf

Q. 3(b) from http://booleweb.ucc.ie/ExamPapers/exams2009/MathsStds/Autumn/MS2001A09.pdf

Q. **2(ii)**, 4 from http://booleweb.ucc.ie/ExamPapers/exams2007/Maths_Stds/MS2001Sum2007.pdf

Q. 6(a) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/MS2001Sum06.pdf

Q. *4(a)*, 6(a) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/Autumn/ms2001Aut.pdf

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

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

Q. 5(a), 6(a) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/ms2001s2004.pdf

Q. 4(a), 6(a) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/MS2001aut.pdf

Q. **3**, *4(a), *5(b), 6(b) from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/MS2001.pdf

Q. *5(b)*, 6(a) from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/ms2001aut.pdf

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

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

*From the Class*

1. *Prove Proposition 5.1.1 in the case that of is an absolute minimum.*

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