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Differential Calculus

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The Associated Student Body (ASB) sponsors a chrysanthemum sale for homecoming weekend with the proceeds going to the scholarship fund. The mums are grown by the Biology Club in campus greenhouses. If ASB sells mums at $3.00 each, they are sure they can sell 600 mums. A student survey shows that for every $0.50 increase, they will sell 30 fewer mums. At what price will the proceeds be the greatest? How many mums should the Biology Club grow? What will the maximum proceeds be?

 

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Find the equations of the tangent lines at the point where the curve crosses itself:
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