Interpretation of a question: "On a triangle"

[Baron]

I recently had a midterm and there was a question that stated "Find the points that could have an absolute maximum or minimum of the function f(x,y) = something, on a triangle with vertices (a,b), (a,c) and (d,c)."

My interpretation of the question was that it wanted me to find points on the perimeter of the triangle that could have an absolute max/min so I didn't bother taking the partial derivatives of f(x,y) and set it equal to zero as that would give me points inside the triangle. All I did was find the boundaries of the triangle, plug it into f(x,y) so f(x,y) only consists of one variable and took the derivative. I set the derivative equal to zero, solved and made sure the points I got were inside the domain.

However my prof's interpretation of on the triangle meant inside the triangle as well.

I disagree with her interpretation because like how on a circle and on a disk are different so is on a triangle and on a triangular region.

So do I have a case?

 

[JeffM]

I recently had a midterm and there was a question that stated "Find the points that could have an absolute maximum or minimum of the function f(x,y) = something, on a triangle with vertices (a,b), (a,c) and (d,c)."

My interpretation of the question was that it wanted me to find points on the perimeter of the triangle that could have an absolute max/min so I didn't bother taking the partial derivatives of f(x,y) and set it equal to zero as that would give me points inside the triangle. All I did was find the boundaries of the triangle, plug it into f(x,y) so f(x,y) only consists of one variable and took the derivative. I set the derivative equal to zero, solved and made sure the points I got were inside the domain.

However my prof's interpretation of on the triangle meant inside the triangle as well.

I disagree with her interpretation because like how on a circle and on a disk are different so is on a triangle and on a triangular region.

So do I have a case?

In my opinion, the question that you have in quotation marks makes no sense whatsoever. Points do not have minima or maxima. "On the triangle" is not unambiguously clear as to whether it refers to the lines delimiting the triangle or the area enclosed by those lines. "Could have" an absolute minimum or maximum: a value either is or is not an absolute maximum or minimum rather than something it could be if just exerted itself.

Is the quotation exact? If so, your professor needs a course in remedial English, but you are unlikely to improve your relationship with her by pointing that out.

 

[Baron]

In my opinion, the question that you have in quotation marks makes no sense whatsoever. Points do not have minima or maxima. "On the triangle" is not unambiguously clear as to whether it refers to the lines delimiting the triangle or the area enclosed by those lines. "Could have" an absolute minimum or maximum: a value either is or is not an absolute maximum or minimum rather than something it could be if just exerted itself.

Is the quotation exact? If so, your professor needs a course in remedial English, but you are unlikely to improve your relationship with her by pointing that out.

Well, the quotation was what I remembered the question as saying so it is not word for word. But it definitely included the words "on the triangle with vertices." The question wanted us to find the list of points that we would normally test/plug into the function to determine whether the point corresponds to an absolute max/min or neither. We were not allowed calculators on the test so I guess that is why the prof didn't want us to find the value, only points that "could" correspond to an absolute max/min.

 

[JeffM]

Well, the quotation was what I remembered the question as saying so it is not word for word. But it definitely included the words "on the triangle with vertices." The question wanted us to find the list of points that we would normally test/plug into the function to determine whether the point corresponds to an absolute max/min or neither. We were not allowed calculators on the test so I guess that is why the prof didn't want us to find the value, only points that "could" correspond to an absolute max/min.

I at least believe "on the triangle with vertices of" is ambiguous as to whether it refers to the perimeter or the area of the defined triangle. There could, however, have been other words in the question that eliminated the ambiguity. If for example the perimeter was formed from constraining equations that represent the domain of the function, then it becomes clearer that area is intended. In which case, a point along the perimeter might be an absolute maximum or minimum without regard to the derivatives.

My guessing what the wording was is not going to help you. Nor is my opinion even if you get the exact wording. It is probably more productive to ask your teacher what she believes to have been in the statement of the problem that precludes your interpretation. Teachers are sometimes reasonable.