Part 4/6:
The graphs illustrate how the tangent line at ( C ) parallels the secant line between the endpoints ( (0, f(0)) ) and ( (2, f(2)) ). Notably, this confirms that at least one point exists—specifically, ( x \approx 1.15 )—where the tangent not only contacts the curve but runs parallel to the secant line.
Example Two: Real-Life Application
To elucidate the theorem's application further, consider a vehicle traveling 180 kilometers in a span of 2 hours. The average speed over this duration is calculated as:
[
\frac{180 \text{ km}}{2 \text{ hours}} = 90 \text{ km/h}
]