To solve this problem, we’re dealing with a tangent line to the function f(x) at the point (4, 3). We need to find the function value f(4) and consider the slope of the tangent line.
First, since the point (4, 3) lies on the function f, we know that f(4) = 3.
Next, we need to determine the slope of the tangent line. The tangent line passes through the point (0, 2) and the point (4, 3). We can calculate the slope (m) of the line using the formula:
m = (y2 – y1) / (x2 – x1) = (3 – 2) / (4 – 0) = 1 / 4.
Since the slope of the tangent line at the point (4, 3) is equal to the derivative of f at x = 4, we find:
f'(4) = 1/4.
This means that at x = 4, the slope of the function f is 1/4. In summary, we have found:
- f(4) = 3
- f'(4) = 1/4
In conclusion, f(4) is equal to 3 and the derivative at that point, which represents the slope of the tangent line, is 1/4.