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# Differentiation Calculus Problems

Posted on 2005-03-12

I'm fairly new to Calculus. Please help me work out the following three questions:-

1.) A swimmer is at a point 500 m from the closest point on a straight shoreline. She needs to reach a cottage located 1800 m down shore from the closest point. If she swims 4m/s and she walks at 6m/s, how far from the cottage should she come ashore so as to arrive the cottage in the shortest point?

2.)A window consists of an open rectangle topped by a semicircle and is to have a perimeter of 288 inches. Find the radius of the semicircle that will maximize the area of the window.

3.)A company determines that its profit equation(in millions of dollars) is given by P=x(cube)-48x(square)+720x-1000, where x is the number of thousands ofunits of software sold and 0<=x<=40. Optimize the manufacturer's profit.

Thanx in advance.