the problem goes as so...find the equation of the line tangent to f(x) = -1/x at the point (3, -1/3). Using the four-step process to find f'(x), I got:
f'(x) = 1/x^2
then using that derivative, i found the slope of the tangent line as f'(3) = 1/3^2 or 1/9.
thus, f(x) is f(3) = -1/3
lastly using y-y0=m(x-x0) i got y + 1/3 = 1/9(x-3)
solving that i got 1/9x -.6 (repeating)
does that sound right? thanks