Ben's Bicycle Helmets makes bicycle helmets at a cost of 3000+ 12x dollars per month to produce x helmets. They sell the helmets for $21 each. 1. Determine the cost to produce 500 helmets. 2. Write an expression to represent the revenue received by selling helmets. 3. Determine the revenue for selling 500 helmets. 4. Write an equation that can be used to determine the break-even point, the point where the revenue costs. 5. Identify the break-even point. 6. Will Ben's Bicycle Helmets earn a profit by selling 500 helmets a month? Justify your response

#1

The cost to produce 500 helmets:

#5

The break-even point is the price when profit is zero:

#6

There will be a profit as the selling price is greater than the break even point:

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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.