Any mathematician to help me answer this question please.. am giving the brainliest

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.

for this case we have that by definition, the volume of a cylinder is given by:

where:

r: it's the radio

h: it's the height

we have as data that:

substituting:

so, the cylinder volume is

option d