You have a large container of olive oil. you have used 22 1/2 quarts of oil. twenty- five percent of the oil remain. how many quarts of olive oil remain

7.5 quarts of olive oil remain.

Let

q = quarts of olive oil remain

25% of olive oil remains means that 75% has been used.

2212 quarts = 22.5 quarts used

22.5.75=q.25

Multiply both sides by .25 to isolate q.

22.5.75(.25)=q.25(.25)

5.625.75=q

7.5=q

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.