Step by step process please Find the tangent line approximat

Step by step process please.

Find the tangent line approximation to the curve at x = 1. Use this approximation to estimate ln (1.1). Is this an under- or over- estimate?

Solution

f(x)= ln x dy= 1/x dx So at f(1) dy= 1/1 dx So when x goes up .1 (from 1 to 1.1), f(x) will go up .1 (from 0 to .1). Since the curve is concave down this will be an overstatement. (Using a calculator ln 1.1= 0.0953)