Okay, so we're writing a test about mathematical analysis tomorrow and I'm pretty fucked if not any of you can explain this secant gradient thing to me.

Like, you got some point on a function's graph and you want to know shit about it, you use that stuff. Basically, I have no idea

• When you use it
  
• Why you use it
  
• and how you use it

Explain, please, if you can.

If you cant translate "Secant gradient" to czech then I can help you.I tried the google translater,but I still dont know whats that.

Well the secant is a straight line that cuts through the graph by hitting two points on it. And the gradient is what leo.org gave me as a translation for well... how steep it is.

the language gap is bad thing :c
i can't help you with it man,sorry

The gradient of a line is its slope. You use it for finding ratios from a straight-line graph, eg, time in ratio to distance. To work it out you take 2 points on the line graph. [see the image] Shit continued after.



Here we have points 'A' and 'B'. The equation X2 - X1 / Y2 - Y1 is used. Replace like algebra and we get 10 - 2 / 5 - 1, then 8 / 4 then 2. The gradient of the line would be 2.

Thats the gradient shit.

I have notes that go into Parabolas which is the graph of a squared un-known. But i can't find any of my notes right now, since the above is from memory you might want to use someone else's incase i ****ed up.

The secant's gradient is used to find an approximation for the gradient of a curve at a point. Keep in mind that gradient is the same thing as slope, rate of change, or derivative at a point. The idea is that by starting with a point P on a curve, and adding a point Q further down the curve, you can draw a secant line between them with a gradient (or slope) near that of the gradient at point P. The closer you move Q to P, the more accurate that approximation becomes.

Here's an image:


By using a secant line, the equation for the gradient (slope) is simple:



Using that and the graph above, you find:
gradient = m = (y2-y1)/(x2-x1) = (4-1)/(3-2) = (3/1) = 3

In the context of point P,Q, and our function, this equation can be rewritten. If we let x equal the x-value of point P, and h equal the distance between point P and point Q, it becomes:



So using that instead:

gradient = m = (f(x+h) - f(x))/h = (f(2+1) - f(2))/1 = f(3) - f(2) = 4-1 = 3


So you use it when you want to find the slope (gradient) at a point on a curve. You use it because you don't know how to take derivatives yet and an approximation is the best you can do :P

ho shit, math **** o____O

My eye's are burning, aaaauugghhhh!!!!.....

no serious **** dude, this is cool math :p

Holy shit, you just saved my ass. Thanks a fuckton, oh holy fucking mother of god, thanks so much.

****, I graduated from what would be the equivalent of college early and I still have no mother of god **** whats going on there.