Mei paints and sells ceramic vases for $35 each. Each month she breaks typically 3 vases in the kin. How much money will she earn if she sells 17?
How many ceramic vases will she need to sell to earn $800?

Ok first of all She need to be careful

$35 for each and if she sells 17

So 35 x 17 = 595

$35 each and she needs $800

Ok so she won’t have $800 exactly but close to it

She could sell 23 vases and get $805

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Answer

1 number

explanation

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.