⦁a park designer wanted to place a fountain so that it was close to both the slide and the swings. refer to the coordinate grid shown. each unit on the grid represents 100 ft. ⦁ ⦁ find the distance from the slide to the fountain. show your work. ⦁ find the distance from the swings to the fountain. show your work

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.