Lin has two small baking pans, each shaped like a rectangular prism. For each question, explain or show your reasoning. Lin lines the bottom of her first pan with aluminum foil. The area of the rectangular piece of foil is 8¼ square in. Its length is 3½ inches. What is the width if the foil?
Show your reasoning.

Explanation is in the file

cutt.ly/nz6VGda

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.