You should say I is an open interval. And ccannotbe an endpoint. Otherwise the limit might not make sense.

Let y!=0 then what is derivative at y, if it exists.C) f(x) = 1/x for x is not equal to 0

(f(x) - f(y))/(x-y) = (1/x - 1/y)/(x-y) = (-(x-y)/xy)/(x-y) = -1/xy

As x--> y we have,

-1/y^2

Thus,

-1/x^2 is the derivative.