This question makes an important point: the maximum point of a function may not always be found by solving f(x)=0. minimum. 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. for every extra tree planted. to 600 peaches. a. Find the function that describes the per-tree yield, Y, in terms of x. Y=Y=ifxisnomorethan30treesperacreifxisgreaterthan30treesperacre b. Find the total yield per acre, T, that results from planting x trees per acre. T= if x is no more than 30 trees per acre T=4 if x is greater than 30 trees per acre c. Differentiate T with respect to x oT /dx=1 dT /dx= b) if x is greater than 30 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 x : trees per acre Maximum yield : peaches per acre Is T differentiable when x equals 30 ? Yes No This question makes an important point: the maximum point of a function may not always be found by solving f(x)=0. minimum. 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. for every extra tree planted. to 600 peaches. a. Find the function that describes the per-tree yield, Y, in terms of x. Y=Y=ifxisnomorethan30treesperacreifxisgreaterthan30treesperacre b. Find the total yield per acre, T, that results from planting x trees per acre. T= if x is no more than 30 trees per acre T=4 if x is greater than 30 trees per acre c. Differentiate T with respect to x oT /dx=1 dT /dx= b) if x is greater than 30 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 x : trees per acre Maximum yield : peaches per acre Is T differentiable when x equals 30 ? Yes No