Crazy... tan... graph? Whaaaat?
Also, with the multiple choice question which described a derivative function (I can't remember which number but it was towards the end)- how can f'(2)=0 and f'(4)=0 and f'(x) between 2 and 4 be positive? How does the graph (of f'(x)) end up back down at 4 if it is increasing in that region? Or is there something I missed in that, which seems to be the only possible explanation?
the answer to that was at x=4 it was a stationary point of inflection
Thanks but I still don't get it. This is how I interpreted it: the gradient graph is shaped like _/_ but the only possible way to do that is to have a point of discontinuity, which would be undifferentiable so you wouldn't be able to get a second derivative to work out the nature of the stationary point.
You had a turning point at x = 4 for the derivative graph which would indicate its a stationary point of inflection... I don't think it was taught in the course, but if you derived the derivative to get the second derivative, you would notice that f''(5) > 0 and f''(3) < 0, and so concavity changes which means its a stationary point of inflection I think.
Also I got 1.21 statues. ^_^