Question

Find and so that has a local minimum at the point , with -coordinate 25?

Answer 1

The tangent line at a point on a curve represents the instantaneous rate of change at that point, and its slope can be determined using the positions of the endpoints relative to the curve, indicating the object's velocity.

Step-by-step explanation:

To find the tangent line to a curve at a given point, you usually calculate the derivative of the function at that point; however, in this case, we already have the endpoints of the tangent line at t = 25 s. These endpoints correspond to positions at different times, which can be used to determine the slope of the tangent line, which in this context is the velocity (v) of the moving object.

1. First, establish the endpoints of the tangent line: 1,300 m at 19 s and 3,120 m at 32 s.
2. Next, use the coordinates of these points to calculate the slope (v) of the tangent line by finding the rise over run, which is the change in position divided by the change in time.