The equation of a curve is y= 1/x
Find the equation of the tangent the curve at the point (2, 1/2).
I am making a mistake but I dont know where! Please help!
So I differentiated the curve and got -x^-2, I input x=2 and got the gradient of -1/4. Then I put the point given and the gradient I found into y-y(2)=m(x-x(2)) and got the eqution of the tangent as y =-1/4x+1. The answers say that its wrong but I dont know where I made the mistake!

Question

The equation of a curve is y= 1/x
Find the equation of the tangent the curve at the point (2, 1/2). 
I am making a mistake but I dont know where! Please help! 
So I differentiated the curve and got -x^-2, I input x=2 and got the gradient  of -1/4. Then I put the point given and the gradient I found into y-y(2)=m(x-x(2)) and got the eqution of the tangent as y =-1/4x+1. The answers say that its wrong but I dont know where I made the mistake!

tommynaut · Answer

Unless if I have also made a mistake, that really does seem to be the correct answer. What do the "answers" give you as the correct answer?

anonymous · Answer

oh....I am really sorry I was looking at the wrong answer :(

anonymous · Answer

So yeah that answer I got was right.

tommynaut · Answer

Yep. Good working out too.

anonymous · Answer

Thanks for your help!