Question

(1 Point) Recall That In Problem 3 Of The Reading Questions For Section 2.1, You Found That If F(X) = Ln(X), Then F'(2) = 1/2. Use This To Find A Formula For The Tangent Line To F(X) = Ln(X) At X = 2. Use this to find a formula for the tangent line to f(x) = ln(x) at x = 2. y=2

Answer 1

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

Explanation:

The formula for the tangent line to f(x) = ln(x) at x = 2 is given by the equation:

y = f'(2)(x - 2) + f(2)

Where f'(2) is the derivative of f(x) evaluated at x = 2, and f(2) is the value of f(x) evaluated at x = 2.

Given that f(x) = ln(x) and f'(2) = 1/2, we can substitute these values into the equation to get:

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

So the formula for the tangent line to f(x) = ln(x) at x = 2 is:

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