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?

Question

anonymous · Answer

kk wait for about five minutes...I tried to draw it here ! but I couldn't

anonymous · Answer

hehe, thanks.

anonymous · Answer

see now...!

anonymous · Answer

thanks neemo, so we're trying to solve for that point that coincided with the curve there?

anonymous · Answer

i guess what i dont get is what does y = f(x) mean here

anonymous · Answer

exactly ! y=f(x) is an equation that "describes" the curve...

anonymous · Answer

so theres the graph itself and the tangent line and we're trying to find a specific point on that tangent line?

anonymous · Answer

also, does y = f(x) just mean that we can solve for y by applying some function to x?

anonymous · Answer

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?

anonymous · Answer

like f(x) = mx+b?

anonymous · Answer

didn't get what you want to say !  x define y ...by y=f(x)....so sorry ; I didn't understand :( !

anonymous · Answer

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

anonymous · Answer

is that accurate?

anonymous · Answer

then; Y0=f(x0) or the point doesn't belong to the curve !

anonymous · Answer

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 !

anonymous · Answer

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?

anonymous · Answer

yes! it is !

anonymous · Answer

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: http://ocw.mit.edu/high-school/

anonymous · Answer

@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!

anonymous · Answer

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'

luvgunn · Answer

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?