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So, in the very first lecture (at the beginning), the professor has "find the tangent line to y = f(x) at P = (x0, y0). Can someone explain what this means exactly?

OCW Scholar - Single Variable Calculus
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kk wait for about five minutes...I tried to draw it here ! but I couldn't
hehe, thanks.
see now...!
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Other answers:

thanks neemo, so we're trying to solve for that point that coincided with the curve there?
i guess what i dont get is what does y = f(x) mean here
exactly ! y=f(x) is an equation that "describes" the curve...
so theres the graph itself and the tangent line and we're trying to find a specific point on that tangent line?
also, does y = f(x) just mean that we can solve for y by applying some function to x?
cuz if i remember my basic algebra, i think we need the slope also, no? or is that assuming the function is providing those details?
like f(x) = mx+b?
didn't get what you want to say ! x define y y=f(x) sorry ; I didn't understand :( !
ok, sorry. think i overcomplicated it. the equation/notation makes sense to me, it just says find the y for the tangent line that hits the curve that has a point of x0, y0
is that accurate?
then; Y0=f(x0) or the point doesn't belong to the curve !
kk now ! I understand ! yeaaah it's true...just notations...finding y=ax+b for the tangent line ! what I gave you ! It satisfies you !
So to summarize, it's asking to get the y for the tangent line that touches a curve with points (x0, y0)? Is that accurate?
yes! it is !
I hope I'm not butting in but you should try watching Highlights of Calculus with Prof Strang, I found it very useful for myself anyway:
@JingleBells, if you are butting in (which i dont think you are) then I'm glad you did! I happened to already be in the middle of reading Strang's book so this is fantastic! Thanks a lot!
I'm glad to be of help. I think Prof Strang is fantastic: he describes \[\Delta y/ \Delta x\]as 'short/short' and dy/dx as 'darn short/darn short'
Hopefully it makes sense now that the proffesor was trying to tell us that derivatives or limits are the slope we need to find first for a given equation to solve or find the equation of a tangent line. Hope that makes sense?

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