Barbara wants to buy soe glittery heart-shaped beads to make friendship bracelets. The beads she wants come in a small pack with 90 beads or a large pack with 300 beads. The small pack costs $3.60, while the large pack costs $9.00. Which pack is the better value?

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.

kaahe btau