See the coversheet for instructions and the point value of each problem.
-
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.
- Find the dimensions of the isosceles triangle
of largest area that can be inscribed in a circle of radius
\(r\).
-
A Norman window has the shape of a rectangle surmounted by a
semicircle. (Thus the diameter of the semicircle is equal to the
width of the rectangle.) If the perimeter of the window is \(30\,
\mathrm{ft}\), find the dimensions of the window so that the greatest
possible amount of light is admitted.
Last modified: Wed Oct 17 18:28:06 UTC 2018