find the slope of a tangent line, i need help!

Question

anonymous · Answer

What do you need the tangent line of?

anonymous · Answer

of this function -1/x

anonymous · Answer

i did the 4 steps but i dont know what to do after i got 2x+h / x (Exponant2) +xh multiple /h

anonymous · Answer

wait hold on lets start from the beginning. You have -1/x and then what?

anonymous · Answer

and i need to find the slope of this function, i got the point (3, -1/3)

anonymous · Answer

So the slope can be found with a derivative right?

anonymous · Answer

yes !

anonymous · Answer

and teh equation for a derivative is $$f'(x)=\lim_{h \rightarrow 0} \frac{ f(x+h)-f(x) }{ h }$$

anonymous · Answer

yes exaclty!

anonymous · Answer

f(x)=-1/x so we get $$f'(x)=\lim_{h \rightarrow 0} \frac{ \frac{ -1 }{ x+h }-\frac{ -1 }{ x } }{ h }$$

anonymous · Answer

oh damn i forget the minus before the first fraction!

anonymous · Answer

so now you get a common denominator and it looks like this$$f'(x)=\lim_{h \rightarrow 0}\frac{ \frac{ -x-(-(x+h)) }{ x(x+h) } }{ h }$$
or just $$f'(x)=\lim_{h \rightarrow 0} \frac{ h }{ h(x)(x+h) }$$

anonymous · Answer

yes i got that answer too!

anonymous · Answer

cancel out the hs in the top and bottom and you get $$f'(x)=\frac{ 1 }{ x ^{2} }$$

anonymous · Answer

yeah exactly ! so my slope is 1/x2, and when i plug 3 in that, it gives me 1/9

anonymous · Answer

Yep and do you remember the point slope equation thing from before?

anonymous · Answer

y-1 = x(x-1/9) or something like that?

anonymous · Answer

y - -1/3 = 1/9(x-1/9)?

anonymous · Answer

Close its $$y-y _{1}=m(x-x _{1})$$ so just change the second 1/9 to 3

anonymous · Answer

ok yeah hold on ill try !

anonymous · Answer

so the answer will be y=1/9x -2/3

anonymous · Answer

?

anonymous · Answer

Yes!! Nice work

anonymous · Answer

jesus haha thanks alot ! it,s been like 5 hours straight that im doing maths haha

anonymous · Answer

Haha. Yah maths is tough stuff.  Is this calc 1?

anonymous · Answer

yes haha u r totally right! yes it is cal 1!

anonymous · Answer

Thats what I'm taking right now!

anonymous · Answer

yeah me too (well that's obvious lol) so ur 17 i guess ? lol

anonymous · Answer

I'm actually 15, i kinda took a couple online courses to get ahead

anonymous · Answer

holy pellet man u r good hahah!!

anonymous · Answer

pellett**

anonymous · Answer

oh sorry the word s** is censured hahahaha

anonymous · Answer

haha lol. Yah thats why im on here to help people out

anonymous · Answer

that's super kind hihi!! :)

anonymous · Answer

Thanks, If you need anything else ill probably be on here pretty regularly. bye :)

anonymous · Answer

ok perfect! bye bye :)!!