14 May 04
how do you find a graphs points of inflection? i know how to find them if it's at a stationary point (gradient of tangent to curve=0) but not when it's not a stationary point...
i got asked to find them in a past paper i was doing, and we've not been toguht how to do it!...and i'm pretty sure it's possible cause there was another answer give apart from the one at the SP...(we had to find the equation of the tangents to the curve at the points of inflection or something 😕)
14 May 04
1 edit
Originally posted by T1000thanks-i tried to look, but i hate google and i think it hates me back too 😞
and genius does not infer knowlegde-maybe i'm a footballing genius? hoever-not once have i claimed to be a genius! my name just infers it...😛
EDIT: and what happened to T1000's post? 😕
14 May 04
Originally posted by geniusThe stationary points are computed by the first derivative of the function. Just compute the derivative and compute when the derivative equals zero. To compute the inflection points, you need the second derivative (it is the derivative of the derivative of the function). Compute when the second derivative equals zero and you have your inflection points.
how do you find a graphs points of inflection? i know how to find them if it's at a stationary point (gradient of tangent to curve=0) but not when it's not a stationary point...
i got asked to find them in a past paper i was doing, and we've not been toguht how to do it!...and i'm pretty sure it's possible cause there was another answer give apart fro ...[text shortened]... d to find the equation of the tangents to the curve at the points of inflection or something 😕)
I hope I explained it well.
Sander
14 May 04
1 edit
Edit: I took so long to type that, it was answered already: well done!When you stationary point, I'm assuming you mean a local minimum (a stationary point being a solution with a local minimum, so that small deviations of the input values tend to cause the system to settle back into the local minimum again, thus the solution is stable).
I'm also assuming you solving for 'Y' with a parameter 'X' (otherwise you also need to consider infinite gradients).
With these assumptions on board, the difference betwen a stationary point and a point of inflection is that with a stationary point, the gradient changes sign through the point in question. With a point of inflection, it goes to zero and then away again without changing sign (taking zero to have no sign).
How to find one? Well, I ain't sure on standard methods, but me, I'd differetiate the whole thing and find local maxima and minima of the differential.
14 May 04
1 edit
Originally posted by geniusArgh, sorry genius! After posting I figured my post was a little cheeky and unfair so asked a moderator (ie me) to remove the badger. In answer to the original questioné, the posts of the tejo-Toe double act above will see you right 🙂
thanks-i tried to look, but i hate google and i think it hates me back too 😞
and genius does not infer knowlegde-maybe i'm a footballing genius? hoever-not once have i claimed to be a genius! my name just infers it...😛
EDIT: and what happened to T1000's post? 😕
14 May 04
Originally posted by ToeMaybe I misunderstood the "inflection points". Toe is right if you mean points like x=0 in the function x^3. The gradient is zero in this point but it isn't a local minimum or maximum. If you mean points where the gradient starts to increase after only decreasing like in x=Pi in the function sin x, or the gradient starts to decrease after increasing (x=0 in function sin x), then you need the second derivative.
When you stationary point, I'm assuming you mean a local minimum (a stationary point being a solution with a local minimum, so that small deviations of the input values tend to cause the system to settle back into the local minimum again, thus the solution is stable).
I'm also assuming you solving for 'Y' with a parameter 'X' (otherwise you also need t ...[text shortened]... but me, I'd differetiate the whole thing and find local maxima and minima of the differential.
14 May 04
are you sure you need to know it? I panicked while sitting my final because a past paper asked several questions I couldn't answer. After fretting for a few days I discovered from a lecturer that the sylabus had changed - the reason I didn't know it was because I hadn't been taught it and it would't be on the exam.
14 May 04
Originally posted by belgianfreakwe definatly haven't been taught it, but the papers actually a model paper and made for htis year-also, we got a question in a past paper asking us to change a base 4 number into base 7. we hadn't been toguht it, but it was in the syllabus 😕
are you sure you need to know it? I panicked while sitting my final because a past paper asked several questions I couldn't answer. After fretting for a few days I discovered from a lecturer that the sylabus had changed - the reason I didn't know it was because I hadn't been taught it and it would't be on the exam.
