There is an archaeological study area located in southwestern new mexico. potsherds are broken pieces of prehistoric native american clay vessels. one type of painted ceramic vessel is called mimbres classic black-on-white. at three different sites, the number of such sherds was counted in local dwelling excavations.

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.

a

step-by-step explanation: