# MATH 2301-102 Fall 2018 Calculus I Recitation 7 Week 10

See the coversheet for instructions and the point value of each problem.

1. For the function $$\displaystyle f(x)= \frac{1}{2}x -\sin(x)$$ on the interval $$0 < x < 3\pi$$:
1. Determine any symmetries.
2. Find any vertical asymptotes.
3. Find the intervals on which $$f$$ is increasing or decreasing.
4. Find the local maximum and minimum values of $$f$$.
5. Find the intervals of concavity and the inflection points.
6. Use the information above to sketch the graph.
2. Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of radius $$r$$.
3. 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.