Caleb usually eats 1 ¼ waffles for breakfast. at a special brunch one day, caleb and seven friends share twelve waffles so that each child gets exactly the same amount. at the special brunch, does caleb eat more or less waffle than usual?

okay so first evaluate 1 1/4 which is 1 waffle and a quarter of a waffle.

so now divide 7 by 12 which is about 1.71 so the answer is yes he ate more than he usually does.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.