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.

On Monday we wrote down the 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).
On Tuesday we did Q. 1 & 2 from the sample. It was clear the sample test is too long and I will ensure that the actual test (Wednesday 8 December) isn’t as long.
On Wednesday we defined what it means for the graph of a function to be 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 a\in\mathbb{R} where the derivative of a differentiable function f:\mathbb{R}\rightarrow\mathbb{R}, f'(a)=0.

When asked to find the critical points of a function defined on the entire real line (rather than just on a closed interval [a,b]), the ‘endpoints’, \pm\infty 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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