Final answer:
The value of f(7) is 2, and the slope of the tangent line f'(7) is 1/7, which is calculated using the coordinate points (7, 2) and (0, 1).
Step-by-step explanation:
We are asked to find the value of f(7) and the derivative f'(7) for the function f(x). The point (7, 2) lies on the curve y = f(x), implying that f(7) = 2. Since the tangent line to y = f(x) at (7, 2) also passes through the point (0, 1), we can use these two points to determine the slope of the tangent line, which is the same as f'(7). The slope m is found by taking the difference in y-values over the difference in x-values.
Using the formula m = (y2 - y1) / (x2 - x1), we get:
m = (2 - 1) / (7 - 0) = 1 / 7
Therefore, f'(7) = 1/7.