Question

Find the equation of the tangent line to the graph of the function f(x) = 2ln(x) + 3 through x = 1?

Answer 1

To find the equation of the tangent line to the graph of the function f(x) = 2ln(x) + 3 through x = 1, find the derivative, substitute x = 1, and use the point-slope form of a line.

Step-by-step explanation:

To find the equation of the tangent line to the graph of the function f(x) = 2ln(x) + 3 at x = 1, we need to find the slope of the tangent line and a point it passes through.

1. Find the derivative of f(x) using the chain rule: f'(x) = 2/x.
2. Find the slope of the tangent line by substituting x = 1 into the derivative: f'(1) = 2.
3. Find the y-coordinate of the point by substituting x = 1 into f(x): f(1) = 2ln(1) + 3 = 3.
4. Use the point-slope form of a line, where the slope is 2 and the point is (1, 3): y - 3 = 2(x - 1).
5. Simplify the equation to get the final equation of the tangent line: y = 2x + 1.