Round the number to hundredths 45.65747

45.66

Step-by-step explanation:

Step 1:  Round to the Hundredths place

45.65747

Since the thousands place is above 5, we round up the hundredths place.

45.65747

45.66

45.66

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.