WILL GIVE BRANLIEST! pls help thank u sm!! :-) u are all amazing

A.

Step-by-step explanation:

When given the following problem,

The problem asks one to find the cube root of the value under the radical. The cube root of a number is essentially a value that must be multiplied by itself three times to get the result under the radical. An easy way to do this is to prime factorize the value under the radical sign. This will allow one to see the components of the number, thus making it easier to take value out of the radical;

Now divide each of the exponents by (3), write the whole result outside the radical, and the remainder under the radical,

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.