Final answer:
The slope (m) is calculated as the rise over the run (Δy/Δx), which is also the derivative of the function at a certain point for curves. The detailed method for finding the slope of a tangent line at a specific point involves using the derivative of the function, which is not provided in the question.
Step-by-step explanation:
The student is asking to find the slope (m) of the tangent line at the point (5, 11). The slope is a measure of how steep a line is, which is calculated by the formula m = Δy/Δx, where Δy represents the change in the y-values and Δx represents the change in the x-values. In other words, the slope is the rise divided by the run. If we have a curve, the slope at any given point is equal to the slope of the line tangent to the curve at that point.
To find this, we can use the strategy that the slope of a curve at a point is equal to the slope of the tangent line at that point. Without the specific function provided, we would typically use the derivative of the function evaluated at the given x-value. However, in the given references, there is an example of finding a slope by determining endpoints and using them in an equation: (260 m/s - 210 m/s) / (51 s - 1.0 s) = 1.0 m/s².
This example shows calculating the slope given two points on the tangent line. Since we are not provided with a specific function or curve in this question, we cannot apply the exact same method. Instead, we would need the function's derivative or additional information to find the slope of the tangent line at the point (5, 11).