Find equation for Tangent line to f(x) = 1/x at x = 1

[kaylamattie]

Find the equation of the line tangent to f(x)=1/x, at the point x=1

Step1 find the derivatieve I come up with
u'=0 and x'1

I come up with slope of 1 since the derivatieve for 1 is zero

Step 2
I get point (1,0)

Kinda confused on this part due to when I plug the numbers in I actual get 1/0 which is undifiened. or should it be 1/1 which would give me (1,1)

Step 3
Y=mx+b
1=0(1)+b
1=b

or
0=0(1)+b
0=b

My equation would be
y=1x+1

Please advise if I'm at least on the right track and if my answer is correct. I a bit lost due to the original problem starting off as a fraction with X on the bottom

Please Help!!!!

 

[galactus]

Re: Find equation for Tangent line

The derivative of 1/x is \(\displaystyle \frac{-1}{x^{2}}\). Therefore, the slope at x=1 would be -1.

Now, you have m=-1 as the slope. You are given x=1. So, plugging that into 1/x, we see the y value is 1.

Use these three values in y=mx+b to so0lve for b and you have it.

x=1, y=1, m=-1