If the quotient of two numbers is positive then both numbers must be positive

true and false if its normal division then yea cuz say if u have 56 divided by 7=8 and 49 divived by 7=7 they are both positive but when u do ratios its diff sometimes the positive way is negative so be careful they always try to trick you

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.