Muhammad has 5 different colors and wantys to color a stip of adjacent squares as in the figure shown, each square with one color. In how many ways can Muhammed do this, provided that no two squares of the same color are adjacent, and the colors of the strip are symmetrical?

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.

this "question" looks more like a project is there any other info you can give me about this. it could be too complex for someone else to do on this website