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I need help with the following homework problem and setting up the equations as well as how to solve them! (Bees collecting pollen and nectar - Optimization) Many bees collect...

It is continuous on [0,2] and differentiable on (0,2) f'(x)=3x^2-4x-2 The thing that I am stuck on is that f(a) does not equal f(b) f(0)=4 f(2)=0   I went ahead and plugged...

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 9-x^2. What are the dimensions of such a rectangle with the greatest possible area?   width=...

A cylinder is inscribed in a right circular cone of height 2 and radius (at the base) equal to 4.5. What are the dimensions of such a cylinder which has maximum volume?   width=??? height=...

If 1300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence...