Kelsey can buy 2 pounds of apples for 7$. Write an equation to represent the cost, c, for a, pounds of apples.

First, we need to find how much a single pound of apples costs.

Do this by dividing.

Now, write an equation.

This represents that the cost equals 3.5 times the number of apples.

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.