If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f '(4)

Answer 1

Since we're talking about the tangent line to y = f(x) at (4, 3), that implies that (4, 3) is a point on the function f.

As such, f(4) = 3.

To determine f'(4), we can simply look at the slope of the tangent line. By definition the slope of the tangent line is the slope at the point (4, 3), which is equivalent to the derivative at the point.

We know that the tangent line includes the points (4, 3) and (0, 2).

To determine slope, we can use the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 3) / (0 - 4)

m = 1/4

Then f'(4) = 1/4.