Question

Given f(x)= ln(x-1)
a. find the equation (in the y=mx+b form) of the tangent to f(x) at x=3
b. find the zeros of f(x) analytically
c. sketch the graphs of f(x) and the tangent line on the same axes
d. write your procedure for finding the zeroes of f(x) graphically
PLEASE HELP AND SHOW ALL STEPS!

Answer 1

a)f(x)= ln(x-1)
f '(x)= 1/( x-1)
f '(3)= 1/(3-1)=1/2, also f(3)= ln(3-1)=ln 2,
using y-y1=m(x-x1)
y-ln 2=(1/2)(x-3), therefore
y=0.5(x-3)+ln2

b)f(x)= ln(x-1)=0
e^ln(x-1)=e^0
X-1=1
X=2 ans....

Answer 2

http://www.wolframalpha.com/input/?i=graph+y%3D0.5%28x-3%29%2Bln2+%2C+y%3Dln%28x-1%29+