Use the graph of f(x) = |x(x2 − 1)| to find how many numbers in the interval [0.5, 0.75] satisfy the conclusion of the mean value theorem.

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.

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !

hi! i think the answer is 1/2 : )