Yeah but from memory the gradient function was something like "square root m -4". Then you had to find the area function (and the terminals for the integral were messed up as well I think) and that would have been really convoluted because you had to integrate with unknowns.
THEN you had to derive area function to find max/min which would have been harder with square root m-4 than a variable "a" or a random positive constant.
If you made it a simple constant like 'a" or a integer value like "1", you make it really easy for yourself in an unfair way because you don't have m or square roots (or whatever) in your area function since your equation is much more simplified.
Debatable. If you REALLY wanted to, you could have just stated 'let gradient = m' and then at the end m for the gradient back into what you got.
If anything, having an explicit gradient potentially makes it easier as there might be a possibility of some simplification involved by virtue of what the gradient is. For instance, if you have derivative of (x^x * f(x)), that's a pain to do normally, but if f(x) happens to equal 2x^-x, the derivative is trivial. See what I mean by possible simplification?