Jennifer buys 4.25 pounds of gummy worms for $2.96 per pound and 0.5 pounds of jaw breakers for $4.95 per pound. Jennifer gives the clerk $20.00. If there is no sales tax on these
items, how much change should she receive?
In money form!

$4.94

Step-by-step explanation:

Gummy worms cost $2.96 per lb, and she bought 4.25 lbs, so:

2.96 * 4.25 = $12.58 spent in gummy worms

Jaw breakers cost $4.95 per lb, and she bought 0.5 lbs, so:

4.95 * 0.5 = $2.48 spent in jaw breakers

Adding the gummy worms and the jaw breakers, she spent:

12.58 + 2.48 = 15.06 in Total

She gave the clerk $20.00, but she only spent only $15.06, so the clerk gave her back the difference:

20 - 15.06 = $4.94 is the change that she received

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.