## 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?

1. Neemo

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

2. levinotik

hehe, thanks.

3. Neemo

see now...!

4. levinotik

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

5. levinotik

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

6. Neemo

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

7. levinotik

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

8. levinotik

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

9. levinotik

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?

10. levinotik

like f(x) = mx+b?

11. Neemo

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

12. levinotik

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

13. levinotik

is that accurate?

14. Neemo

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

15. Neemo

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 !

16. levinotik

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?

17. Neemo

yes! it is !

18. JingleBells

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/

19. levinotik

@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!

20. JingleBells

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'

21. Luvgunn

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?