Solving for f(2) Given Tangent Line Information
The question is asking for the value of f(2) given that the tangent line to the graph of y = f(x) at the point (2, 4) passes through the point (-1, 3).
To solve this, we can use the fact that the slope of the tangent line at a point on a curve is equal to the derivative of the function at that point. The slope of the tangent line can be found using the two points it passes through: (2, 4) and (-1, 3).
The slope (m) of the line passing through these two points is given by:
m = (y2 - y1) / (x2 - x1)
Substitute the given points into the formula:
m = (3 - 4) / (-1 - 2)
m = (-1) / (-3)
m = 1/3
Now, because the slope of the tangent line to the curve at the point (2, 4) is also the derivative of the function at x = 2, we can say that:
f'(2) = 1/3
Since the point (2,4) lies on the tangent and hence on the graph of the function, we know that f(2) = 4. The question seems to be mistaken or poorly phrased because it's asking for f(2), which we already know is 4 from the given point (2, 4) on the graph of the function.
Hence, f(2) is 4.
