ScottHann
Jun 8, 2012, 07:08 PM
Use the equation of the tangent line to approximate values for ln (9.1) and ln (10).
Use the graph of f(x) to determine whether the approximate values are smaller or larger than the true values.
ebaines
Jun 11, 2012, 02:21 PM
The tangent line can be found using
y - y_1 = m(x-x_1)
where (x_1,y_1) is a known point on the line and m is the slope. In this case you know that the point (9, ln 9) is on the line, and the slope is the derivative of the y=ln(x) curve at x = 9. The derivative of ln(x) is 1/x, so at x = 9 that equals 1/9.
Once you have the equation for this line plug in x=9.1 and x = 10 and see what you get.
Post back with your answers and we'll check them for you.