Slope Unity in Mean Value Theorem: Average Meets Instant
The Mean Value Theorem states that for a continuous and differentiable function, there exists a point where the function’s slope equals the average rate of change over an interval. The Mean Value Theorem is crucial for:
Average Value of a Curve
The average value of a function over an interval \( [a, b] \) is computed as the integral of the function over that interval, divided by the interval’s length. This yields the function’s mean value, representing its average height on the interval \( [a, b] \).
