Question

Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = In(x), then ƒ'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = = In(x) at x = 2.

Answer 1

Answer: y - ln2 = (1/2)(x - 2) or y = (1/2)x + ln2 - 1

Explanation:

f(x) = lnx

f'(x) = 1/x

f(2) = ln 2 , so we have the slope = 1/2, and a point (2, ln2)

equation of tangent:

y - ln2 = (1/2)(x - 2)

y = (1/2)x + ln2 - 1