Ned, the owner of Ned's Nut Shop, sells peanuts for $7 per pound and cashews for $6 per pound. Ned wants to create a 20 pound barrel of mixed nuts and sell it for $6.65 per pound. How many pounds of peanuts and cashews should Ned use?

ok

step-by-step explanation:

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.