Final answer:
To find f(6) and f '(6), we need to use the fact that the tangent line to y = f(x) at the point (6, 2) passes through the point (0, 1). To find f '(6), we can use the slope of the tangent line, which is the same as the slope of the function at that point. However, without more information about the function f(x), we cannot determine the exact value of f(6).
Step-by-step explanation:
To find f(6) and f '(6), we need to use the fact that the tangent line to y = f(x) at the point (6, 2) passes through the point (0, 1).
1. To find f '(6), we can use the slope of the tangent line. The slope of the tangent line is the same as the slope of the function at that point. We need to find the slope of the tangent line using the two given points.
2. The slope of the tangent line is given by:
(y2 - y1) / (x2 - x1)
3. Plugging in the values, we get:
(2 - 1) / (6 - 0) = 1/6
4. So, f '(6) = 1/6.
5. To find f(6), we can substitute x = 6 into the equation y = f(x).
6. However, since we only have the slope of the tangent line, we cannot determine the exact value of f(6) without more information about the function f(x).