Question - Solving for f(2) Given Tangent Line Information
Solution:
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 = 1/3Now, 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) = 1/3Since 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.
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