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levinotik
 3 years ago
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?
levinotik
 3 years ago
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?

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Neemo
 3 years ago
Best ResponseYou've already chosen the best response.1kk wait for about five minutes...I tried to draw it here ! but I couldn't

levinotik
 3 years ago
Best ResponseYou've already chosen the best response.0thanks neemo, so we're trying to solve for that point that coincided with the curve there?

levinotik
 3 years ago
Best ResponseYou've already chosen the best response.0i guess what i dont get is what does y = f(x) mean here

Neemo
 3 years ago
Best ResponseYou've already chosen the best response.1exactly ! y=f(x) is an equation that "describes" the curve...

levinotik
 3 years ago
Best ResponseYou've already chosen the best response.0so theres the graph itself and the tangent line and we're trying to find a specific point on that tangent line?

levinotik
 3 years ago
Best ResponseYou've already chosen the best response.0also, does y = f(x) just mean that we can solve for y by applying some function to x?

levinotik
 3 years ago
Best ResponseYou've already chosen the best response.0cuz if i remember my basic algebra, i think we need the slope also, no? or is that assuming the function is providing those details?

Neemo
 3 years ago
Best ResponseYou've already chosen the best response.1didn't get what you want to say ! x define y ...by y=f(x)....so sorry ; I didn't understand :( !

levinotik
 3 years ago
Best ResponseYou've already chosen the best response.0ok, 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

Neemo
 3 years ago
Best ResponseYou've already chosen the best response.1then; Y0=f(x0) or the point doesn't belong to the curve !

Neemo
 3 years ago
Best ResponseYou've already chosen the best response.1kk now ! I understand ! yeaaah it's true...just notations...finding y=ax+b for the tangent line ! what I gave you ! It satisfies you !

levinotik
 3 years ago
Best ResponseYou've already chosen the best response.0So to summarize, it's asking to get the y for the tangent line that touches a curve with points (x0, y0)? Is that accurate?

JingleBells
 3 years ago
Best ResponseYou've already chosen the best response.0I 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: http://ocw.mit.edu/highschool/

levinotik
 3 years ago
Best ResponseYou've already chosen the best response.0@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!

JingleBells
 3 years ago
Best ResponseYou've already chosen the best response.0I'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'

Luvgunn
 3 years ago
Best ResponseYou've already chosen the best response.0Hopefully 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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