Applied Differentiation Question

[hawkrook]

I'm not sure how to respond to d. In the domain 0 to 1, x = 0 will give the maximum area, but the question specifies 'if two squares are formed' and if x = 0 then only one square will be formed because it will be impossible for a square to form from a string with length 0. So then wouldn't that the maximum area would be achieved when there are two squares when x = something like 0.0000000001. So how would  I answer the question?

[dokk]

The answer you have is correct, as it is the maximum possible area of the two squares. Because it is a maximum, it can't be any larger. The question asks 'if two squares are formed but x is an element of [0,1]...', so it only implies that there are two squares, but because of the domain/restriction, there's a chance there isn't, which in this case is true. It is also proven by your answer (can't have length 0).

So for your answer, you would write the area, but you would specify that only one square would be formed.

[lifeisgood]

i literally did this question last week. its actually quite easy.
f(0) this is when x =0 (this comes from the domain [0,1]
max area would be calculated by subbing into the original equation
1/8 (0^2-10*2+50) =6.25 or 25/4
max area would be 6.25 but only one square would be formed