That's something I have never thought off before3) dy/dx = 0 at x = 0
4) dy/dx = 0 at around x = 2.5
(ii)
You have four pieces of information to use:
1) y = 0 at x = 0
2) y = 0 at x = 3
3) dy/dx = 0 at x = 0
4) dy/dx = 0 at around x = 2.5
, and then I am stucked, I don't have the answer yet, it's an per exam exercise, I will need to wait until Monday to ask my tutor for the answer.y = a(x-3)x^2, a<0
My first impression is that it is a cubic expression of the form:
\(
y = a(x-3)x^2
\)
You can't get the value of 'a' beyond noting that it must be negative. The sign of 'a' determines whether the graph you get is the one on the page or one that is mirrored about the x-axis. But the magnitude of 'a' determines the vertical scaling and there is absolutely no vertical scaling information given in the graph. You don't know if the peak at x=2 occurs at a y value of 1 or 1000 or 0.0001. Given that value, you can determine the value of 'a', otherwise it has to remain a negative constant of arbitrary magnitude.I assumed I will need to get the value of a too, but I am out of ideas.
Good plan! Sure wish I had been smart enough to follow that route when I was at that point in my life.My plan is stick to my own answer but not to argue with my tutor
The answer is not incomplete. It is the question that is incomplete. The question needs to be clear about assumptions for the function. However, the assumptions that lead to this answer are very reasonalbe ones to make in the absence of a rigorously clear question.The answer I got from my tutor is:
Y=-x^2(x-3)
But I think it's incomplete
I'm gonna disagree with you on this one. The question may be incomplete, but the answer still needs to match the question. If someone asks me how much gasoline they need to drive 1000 miles in their car, I can tell them that they need 1000mi/M where M is their car's gas mileage. It would not be correct for me to arbitrarily set "M equal to 1" (1mpg, that is) and say that the "complete answer" is 1000 gallons. Or, using the example I used earlier, if the question is to take the integral of 2x (perhaps stated something like, "What function of x has a slope that is everywhere equal to 2x?", an answer of x^2 can't be claimed to be a "complete answer" to an incomplete question. If the question is defined only to within an arbitrary constant, then the answer needs to reflect the existance and influence of that constant.The answer is not incomplete. It is the question that is incomplete. The question needs to be clear about assumptions for the function. However, the assumptions that lead to this answer are very reasonalbe ones to make in the absense of a rigorously clear question.
I can find many other answers to the question that are not the same as the one you suggested. So, your answer does not match the question any better than the tutor's does. You have made specific assumptions about the question and hence feel your answer is complete. The tutor did the same. The fact that your answer is more general than the tutor's does not mean that someone else does not have an answer that is more general than yours.I'm gonna disagree with you on this one. The question may be incomplete, but the answer still needs to match the question.
I'll grant you that. In any question like that there is virtually always the unstated goal of using the "simplest" solution possible, but as I remarked in another thread, what is the metric by which "simple" is judged? Having said that, the heart of most of these types of questions is whether or not the person can make the "correct" initial assumption about the basic form of the underlying equation.I can find many other answers to the question that are not the same as the one you suggested.
I'm not sure I'll grant you that, but I definitely understand your point.So, your answer does not match the question any better than the tutor's does.
That's what I got, though I may have come at it from a different direction. I started with a generic decaying exponential and fit the two points. The result reduces to your solution. That same solution can reasonably be arrived at by inspection.For the second one, I would suggest the following, but there are alternatives.
\( y={{2}\over{20^{x/3}}}\)
he starts off with the assumption of it's exponential equation with a base of e, however, I personally like the answer of:y=2e^(-x)
this answer makes more sense to me, can you explain how did you get this answer please? thanksy=2/(20^(x/3))
If you believe that solutions to these types of questions should provide exact matches to the data values given, then this is wrong. If you are willing to settle for numerical approximations that are close, then this is almost certainly close enough.the answer given by my tutor is:
\(
y = 2e^{-x}
\)
An exponential equation is an exponential equation, the choice of base is arbitrary and merely introduces a scaling factor.he starts off with the assumption of it's exponential equation with a base of e
The tutor's method is correct, but the answer is not mathematically exact, hence making it wrong in most math contexts. It might be good enough for engineering or science purposes, but the constant k is not exactly equal to one.this answer makes more sense to me, can you explain how did you get this answer please?
To WBahn:If you believe that solutions to these types of questions should provide exact matches to the data values given, then this is wrong. If you are willing to settle for numerical approximations that are close, then this is almost certainly close enough.
by Luke James