Ineed on how to solve these problems ( do not give me the answers i just want to learn how to solve these types of problems : )) part a: find a rational number that is between 7.7 and 7.9. explain why it is rational. part b: find an irrational number that is between 7.7 and 7.9. explain why it is irrational. include the decimal approximation of the irrational number to the nearest hundredth.

For part A, all you need to do is find an number between 7.7 and 7.9 but the number must terminate, or end.

For part B you must find a number that does not end and does not repeat, but round that number to the nearest hundredth.

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.

the answer would be c