Proving Max points necessary? (1 Viewer)

[Frie]

I notice that in some of the sample answers of past exams, for questions like "Hence show the maximum area is ... cm^2", the sample answers include an area where the person actually tests that it is a max, by testing 1 up and 1 down.

Is that test actually necessary? Because I have never gotten into the habit of doing it and the question just says show the maximum area is "[insertmaxarea]" , not prove it is the max area.

Edit: yeah i think i messed up thread title. but it's more of a generic thing about questions relating to what is said above.

 

[andybandy]

if it ask you to prove its a max point, you have to prove the stationary point is a maximum, by either second derivitave or a change in gradient

 

[Frie]

Yeah, if it explicitly tells you to prove it, of course I will. But like, what if it says show that max is "bla bla bla".

 

[andybandy]

what do you mean? can you give an example of a question ?

 

[bedpotato]

Yes, you do.

 

[Trebla]

Yeah, if it explicitly tells you to prove it, of course I will. But like, what if it says show that max is "bla bla bla".

Just because the question mentions that it is a max, doesn't mean you can assume it is a max because you're really just using the answer to get to the answer. The question says 'show' so you have to prove it is a max.

 

[Frie]

Just because the question mentions that it is a max, doesn't mean you can assume it is a max because you're really just using the answer to get to the answer. The question says 'show' so you have to prove it is a max.

Alright thanks, I'll try keep that in mind tomorrow

 

[Frie]

There was a question that was "Find the minimum distance between the cars" today, were we meant to prove it was minimum, cause I didn't want to spend a lot of time, and just left that out but I think I got the distance right.

 

[bedpotato]

There was a question that was "Find the minimum distance between the cars" today, were we meant to prove it was minimum, cause I didn't want to spend a lot of time, and just left that out but I think I got the distance right.

Yes you did. All you had to do was find the second derivative. Since it was just a number, you didn't even have to sub t into it to prove it's a minimum.

 

[Recondit]

I was taught to always show it via second derivative or first derivative table