On Monday we completed our introduction to horizontal asymptotes and vertical asymptotes.

On Wednesday we did some examples of curve sketching and applied max/ min problems.

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

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.

Other Exercise Sheets – Questions on Asymptotes

From section 4 Q. 5 from Problems, find the vertical asymptotes of the the functions 5(b) [(7-10), (13), (15-16), (23)] and Q. 5(c) [except (30-31)]

Past Exam Papers

Q. 2(a), 6(b) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001Aut05.pdf

All of this except Q. 1(d) [this is the Autumn 2010 paper which wasn’t on the library website earlier in the year]

http://booleweb.ucc.ie/ExamPapers/exams2010/MathsStds/Autumn/MS2001Aut2010.pdf