Question

an orchard involving a particular type of fruit tree the average weight of fruit w kg produced per tree depends on N the number of trees per 100 m square according to the rule w=(600-15n) for 11<n<26 using calculus and clearly justifying that your value would indeed give a maximum determine the value of n that gives the maximum total weight of this fruit that produced per 100 m square

Answer 1

total fruit per square is just #trees * avg weight per tree, or
f(n) = n*w(n) = 600n-15n^2
f'(n) = 600 - 30n
maximum occurs when f'(n)=0, or n = 20
Note that n=20 lies in the domain of the function.
You can either use what you know about parabolas to realize that this one opens down, so any f'=0 will be a maximum.

Or, you can use f"(n)=-30 to show that the curve is concave down, making the extremum a max.