Slope Unity in Mean Value Theorem: Average Meets Instant
finding the average rate of change for the interval \( [a,b] \) using the formula \( f'(c) = \frac{f(b) – f(a)}{b – a} \) finding the derivative of the function using rules of differentiation setting the derivative equal to average rate and solving for \( x \), which will be the coordinate of the \( […]
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 \( [a, b] \).
