Without using derivatives, and since the graph is the same for y = ax^2, I would set the equation for the slope at (x_0,y_0) equal to f(x) and solve for m. I'm pretty sure this problem can be solved with power series and vector analysis as well. 

I just discovered quite a neat little thing which has made me happy. I thought it'd be cool to set it as a puzzle; you only need elementary mathematics. Also it'll be interesting to see if people have ever been taught this (I've never seen it). When you get it, it's very satisfying to watch how all the algebra comes together. 

Last edited by Xei; 07022010 at 12:50 AM.
Without using derivatives, and since the graph is the same for y = ax^2, I would set the equation for the slope at (x_0,y_0) equal to f(x) and solve for m. I'm pretty sure this problem can be solved with power series and vector analysis as well. 

Last edited by Phion; 07012010 at 01:42 PM.
I don't know what you mean. How do you know what the slope is at (x0, y0) without calculus (patently it's 0 but that's not thorough, and I don't see how it helps find the slope anywhere else). 

Last edited by Xei; 07012010 at 10:55 PM.
I've never heard of expressing the gradient of a function before. Is that a linear algebra thing? 

Really? We were introduced to this in school when I was 15. The term is differentiation. 

Last edited by Xei; 07022010 at 12:32 AM.
Huh, I've seriously never heard of differentiation referred to as finding the gradient of a function before. Maybe it's just because I'm schooled in the U.S.? I've gone through calc 1 and 2 (there are 3 levels that are taught for calculus here, the third of which I'm taking in the coming year, and I'm not sure how that differs from Europeantaught math). I wasn't aware that the derivative of a curve could be found without the use of calculus either.. I'll give it some thought. 

Weird... all it means is 'the gradient of the tangent to the curve at x'; does that make sense to you? 

Otherwise known as the slope of the curve at x, in which case it does make sense to me. 

Ah okay. Yeah, things like 'slope' and 'rise over run' I've only ever heard from Americans I think. 

You mean instead of x_{0} and x_{l}? We usually only use those if we're talking about integration between two points, or in physics to denote the initial and final state of something that occurs over time. If x is just one arbitrary value, it typically just stays x. 

Nah I mean handwritingwise. We do 'em curly. 

I would set the formula for slope equal to the quadratic, 

Last edited by Phion; 07022010 at 03:08 AM.


Its actually possible to graduate collage with just algebra level math in the US. Unless you are studying math or science, people really neglect math. I always thought it was silly, that in high school you are only required to take a math class two out of the four years. Of course any one who is serious takes it all four years. 

What's graduating college; 18 years old? 

Well in the US you go to school until your 18, then collage is normally 4 years after that if you want a basic degree(which is of course optional). So technically you could be in school until you are 22 get a bachelors degree in say arts, and you never got passed algebra. 

High school in the U.S. ends at about 18 years of age, yar. College can also be as short as two years if one is only going to receive "general education" credits or trade skills at a community college (the cheap alternative to universities). Some high schools, at least in California (or maybe just in the district I'm in) a minimum of three years of math classes are required. 

A power series is an infinite sum of terms in a sequence with a very specific multiplier of the form (xa). 



Last edited by Xei; 07022010 at 05:53 AM.
Yea, I'll be finishing up two certificates in computer science this year (only 60 credits total), then after that I'll be going back to obtain a transfer degree in physics/engineering, which I should have gotten almost a year ago, to a university in the state of Illinois. I slacked off quite a bit in high school, but I've done a pretty good job at making up for it. 

What about zs? :V 

Let's be friends. 

Bookmarks