Final answer:
To estimate the slope of a tangent line to a curve at a specific point, identify two points on the tangent line and calculate the slope using the rise over the run between these points.
Step-by-step explanation:
The slope of the tangent line at a given point on a curve is found by determining the ratio of the rise over the run between two points on the tangent line. For the function f(x) at x = -1, we estimate this by using the slopes of secant lines close to the point where the tangent touches the curve. The slope of the curve at a specific point, such as t = 25 s, is the same as the slope of the tangent line at that point.
You should begin by identifying two points on the tangent line. For example, if you find that the endpoints of the tangent line at t = 25 s correspond to a position of 1300 m at time 19 s and a position of 3120 m at time 32 s, these can be used to compute the slope. To do this, use the formula:
Slope (v) = (final position - initial position) / (final time - initial time), which in this case gives v = (3120 m - 1300 m) / (32 s - 19 s).