Given that for ,
(a) obtain an expression for f′ (x), [4]
(b) find the x-coordinate of the stationary point on the graph of f and determine whether this point is a maximum or a minimum. [4]
Now for the first part, I obtained a derivative of
through logarithmic differentiation. I think this is correct, but the problem I have is knowing what to do in the second part of the question. How would you go about finding the x-coordinate and how can you tell what kind of point it is?
Thanks again for your time and patience
So would I take of the derivative I obtained?
It seems a very complicated function and I would find that enormously difficult to even attempt! Would you describe it as a lengthier process than the first, because both parts of the question are worth 4 marks each and the second part sounds like a higher volume of work
I like your idea of plugging in a value I couldn't cheat as this would be for an exam which doesn't allow graphic calculators - on my course syllabus it says nothing about taking second derivatives (It is an A-Level course for further maths) so I assume that plugging in values must be what they are asking for
I plugged in x=1 as I recognised that ln 1 = 0 so thought that would automatically make the rest of it zero - but then I checked it and it did not mean this was the case, as it is only being subtracted from something else.
I'm struggling here but I hope I can learn how to answer it using your recommended method of second derivatives - I can only do this with basic/parametric equations but f'(x) in this question looks beyond my ability to differentiate a second time.
I actually used that site to validate the first derviative that I took and I had a look to see what the second one would be, but that is far beyond my capability which is why I find it difficult I did try, and took logs of both sides and I couldn't find a way to get any further. Sorry but I'm not sure the question is looking for the answer through those methods - maybe the plugging in the values that was suggested? How would you go about doing that? I have never done this before and I would like to know how
This method is EXTREMELY sketchy. The concept is this. Having found a critical point of we can assume (by the way the question is worded) that is either a local maximum or local minimum. To determine which it is take and compare it to for some arbitrarily small . The sketchiness is that if you use was it small enough.
I see what you mean. I've tried this value and also some smaller values and none of them come close to equating to zero. The question seems to be looking for a very particular answer and it sounds definitely very hit and miss.
The question is on this past paper, just for you to get a bit of background:
http://www.wjec.co.uk/uploads/papers/w08-977-01.pdf it's the ninth and last question on the paper. I just have this feeling that I'm missing something completely obvious but I don't know what it is
I now interpret what you mean as inserting a small value as x and seeing whether it is positive or negative - I put in 0.2 and got a negative value, which would mean that it is a maximum point?
Sorry if I have misunderstood again, it must be frustrating but I massively appreciate your help