In deductive reasoning, you start from a set of rules and conditions to determine what must be true.

The correct answer is:

B) given.

Explanation:

Deductive reasoning is called top-down reasoning. It starts with given rules, theorems, etc. and uses these to prove that other statements are true.

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.