A life guard on a beach needs to get to a swimmer in the water that is 200ft down the shoreline and 100ft out from the shore. The life guard can run 10ft/sec on the beach and can swim 4ft/sec in the water. To get to the swimmer in the least amount of time, how far should the lifeguard run down the beach before swimming out to the swimmer in the water? Approximate your answer to the nearest hundredth.

A rectangle (blue in picture) has its bottom left corner on the origin, and its top right corner is on the graph of the quarter-ellipse (black in picture), . Find the dimensions of the rectangle that maximize the area of the rectangle.

What are the global maximum and global minimum values of the function .

Locate any points of inflection for the function:

Find the maximum value of on the interval .

It's Mother's Day and you want to make a wonderful picture for your mom. You know that you will put a nice ribbon on the border of your rectangular picture, and that you will put double ribbons on the left and right sides. You have 80 inches of ribbon. What dimensions should your picture have if you want it to have the most area possible without running out of ribbon?

Given the function ,

find at .