Question

How do I do this question: find slope of the curve y=1/(X-1) at X=2. I don't get the algebra here, how is it equal to -1?

Thanks

Answer 1

Oh and please do not answer with derivatives. Need to use the (f(x-h)-f(x))/h

Answer 2

well, just plug and chug.

f(x+h)-f(x) = 1/(x+h-1) - 1/(x-1)
= ((x-1)-(x+h-1))/((x-1)(x+h-1))
= (x-1-x-h+1)/((x-1)(x+h-1))
= -h/((x-1)(x+h-1))

Now, divide that by h, and you have

-1/((x-1)(x+h-1))

Now you can take the limit as h->0, and you end up with

-1/(x-1)^2

at x=2, that is -1