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This question makes an important point: the maximum point of a function may not always be found by solving f(x)=0. may not even have a maximum or minimum. relative max. or relative min. that can be found by solving f(x)=0.) Two parts of this question are multiple choice: you only get one submission attempt for those two parts. A peach orchard owner wants to maximize the amount of peaches produced by her orchard. decreases by 40 peaches per tree for every extra tree planted. 35 ) peaches, which is roughly equal to 800 peaches. a. Find the function that describes the per-tree yield, Y, in terms of x. Y= if x is no more than 35 trees per acre Y= if x is greater than 35 trees per acre b. Find the total yield per acre, T, that results from planting x trees per acre. T= if x is no more than 35 trees per acre T= if x is greater than 35 trees per acre c. Differentiate T with respect to x dT/dx= 3) if x is less than 35 trees per acre dT/dx= 3 if x is greater than 35 trees per acre Does this derivative ever equal zero? No Yes d. Sketch the graph of T as x varies and hence find the value of x that maximizes the yield and the maximum value of the yield. Optimal value of . * trees per acre Maximum yield : peaches per acre Is T differentiable when x equals 35 ? Yes No

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