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