Find the LCM of 36 45 63 and 80

36 = 2*2*3*3

45 = 5*7

63 = 3*3*7

80 = 2*2*2*2*5

Then take each unique factor (2, 3, 5, and 7) and raise each the greatest power it has in any of the input numbers (2^4, 3^2, 5^1, 7^1) and multiply them, and that is your answer.

2*2*2*2*3*3*5*7 = 5040

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.