Ted and Robin each gave a basket of green apples to their friend Lily. Ted’s basket contains 5 apples, each weighing ounces. Robin’s basket contains 6 apples, each weighing ounces. Whose basket is heavier and by how much?

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.

the answer is:

mean: 6

mad: 2.14