Proving maximum/minimum points - shortcut methods? (1 Viewer)

[sHin]

For the past 3 years, Q10 of the exam has included some messy looking algebra questions where you're required to prove that a point is a max/min. I was just wondering.. what is sufficient in proving a point is i.e. subbing in values either side of f'(x), using f''(x)

For example.. attached is a sample answer for Q10 of the 2003 paper. Is drawing up a table and simply indicating positive/negative on either sides of the stationary point sufficient?

 

[withoutaface]

I think unless its a messy differentiation you're better off using f''(x), but either should be fine.

 

[Lazarus]

Is drawing up a table and simply indicating positive/negative on either sides of the stationary point sufficient?

Yes.

But notice that they've also written a concluding statement - "therefore maximum occurs at x = blah".

Do that too, as it demonstrates that you actually know what the table means.

 

[Li0n]

I think unless its a messy differentiation you're better off using f''(x), but either should be fine.

agreed, only if i cbf finding f"(x) do i do the table thingi

and you ALWAYS have to do the "therefore max point"
i remember i lost a mark for just stoping at f"(x) > 0 or whatever

 

[~ ReNcH ~]

I notice in solutions that in the tables they only put | -ve | 0 | +ve |, whereas I tend to evaluate it everything even if I know it will be a minimum or maximum before even doing the test. Do you really have to place a value in the table, or can you just rort it and say <0, 0, >0 without evaluation?

 

[~*HSC 4 life*~]

I notice in solutions that in the tables they only put | -ve | 0 | +ve |, whereas I tend to evaluate it everything even if I know it will be a minimum or maximum before even doing the test. Do you really have to place a value in the table, or can you just rort it and say <0, 0, >0 without evaluation?

no guys, you have to write down the actual value you get, you wont get full marks if you fudge it

 

[~ ReNcH ~]

no guys, you have to write down the actual value you get, you wont get full marks if you fudge it

Do you actually get marks for getting the right value when you test for the nature of the stationary point?

 

[Xayma]

If is multiple's like f'(x)=(x-5)(5x+6) then you could go +-=-ve

But if its addition/subtraction you will have to evaluate it.

 

[Estel]

In some cases, it's also necessary to evaluate the boundary points.