PLEASE HELP there are just as many square numbers as there are counting numbers. you can see that because you can match the squares up with the counting numbers, and you never run out of either. but doesn't it seem that there must be more counting numbers than squares since not every number is a square?

i think its a yes

Step-by-step explanation:

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.