See the coversheet for instructions and the point value of each problem.
 Sketch the graph of a single function that has all of the
following properties:
 Continuous and differentiable everywhere except at \(x=3\),
where it has a vertical asymptote.
 A horizontal asymptote at \(y=1\).
 An \(x\)intercept at \(x=2\).
 A \(y\)intercept at \(y=4\).
 \(f'(x) \gt 0\) on the intervals \((\infty,3)\) and \((3,2)\).
 \(f'(x) \lt 0\) on the interval \((2,\infty)\).
 \(f''(x) \gt 0\) on the intervals \((\infty,3)\) and \((4,\infty)\).
 \(f''(x) \lt 0\) on the interval \((3,4)\).
 \(f'(2)=0\).
 An inflection point at \((4,3)\).

For the function \(\displaystyle f(x)= \frac{\sqrt{1x^2}}{x}\):
 Find the domain.
 Find the intercepts.
 Determine any symmetries.
 Find any asymptotes.
 Find the intervals on which
\(f\) is increasing or decreasing.
 Find the local maximum and minimum values of
\(f\).
 Find the intervals of concavity and the inflection points.
 Use the information above to sketch the graph.
[This is section 4.4 #21; you can check your answer in the back of the book, but you need to show how to get to the answer.]

For the function \(\displaystyle f(x)= \frac{1}{2}x \sin(x)\) on the interval \(0 < x < 3\pi\):
 Determine any symmetries.
 Find any vertical asymptotes.
 Find the intervals on which
\(f\) is increasing or decreasing.
 Find the local maximum and minimum values of
\(f\).
 Find the intervals of concavity and the inflection points.
 Use the information above to sketch the graph.
[This is section 4.4 #31; you can check your answer in the back of the book, but you need to show how to get to the answer.]
Last modified: Fri Oct 27 14:56:40 UTC 2017