Mean Value Theorem - AP Calculus - Lecture Notes, Study notes of Calculus

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Calculus Section 4.4B Notes Learning Targets... 1. Find the average value of a function on an interval 2. Apply Mean Value Theorem (MVT) for integrals 3. Find the area of a region using integration LT: Find the average value of a function on an interval e The average value of a function f on [a,b] is: sal ‘food = Find the average value & any points on the interval where the value is equal to the average value. 1) f(x) =4—x?7; [0,3] 3 \ (4- x) 8x 4y-x = | 2 ui 3 > =K +fi2-) = ) — Gass we C3) LT: Apply Mean Value Theorem (MVT) for integrals e There is some value c, such that... D e In other words: There is a rectangle with the same area & base as the integral. The top of the rectangle intersects the curve of the function at x = c. e Note: f(c) is the average value of the function (constant). rnd the value of c guaranteed by the MVT for integrals. ) Fa) = ; [1,3] 1/2