Question

given f(x)=ln(x-1). find the equation of the tangent to f(x) at x=3, find the zeroes of f(x) analytically, sketch the graphs of f(x) and the tangent line on the same axes, write your procedure for finding the zeroes of f(x) graphically. please help and show all steps!

Answer 1

I think
d(ln (u ))/dx = i/u (du/dx)
so f'x = 1/(x-1)* d((x-1))/dx = 1/(x-1) * 1
so f'x = 1/(x-1)
at x = s
slope = 1/(3-1) = 1/2
I have no idea what the zeros of f(x) means

Answer 2

I meant at x = 3 (stupid dyslexia!)