Annual profit in thousands of dollars is given by the function, P(x) = -.01x2 + 50x + 30,000, where x is the number of items sold, x ≥ 0. will this profit function have a maximum? if so what would it be?

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Annual profit in thousands of dollars is given by the function, P(x) = -.01x2 + 50x + 30,000, where x is the number of items sold, x ≥ 0. will this profit function have a maximum? if so what would it be?

Mathematics
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would i use the formula x=-b/2a
you can derive it to get the maximum y'=-.02x+50 try getting the critical points -.02x + 50 = 0 50=.02x x= 2500 get the y y= -.01(2500)^2 + 50(2500)+30000 y= -62500 + 125000 + 30000 y= 92500 the function has a maximum 92500 at x = 2500
that is what i got

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so the max weekly profit is approx 92,500 when 2,500 units are sold
yes ^^
so then what steps should the company do to prepare for my answer which was 92,500 was the max weekly profit when 2,500 units are sold?
can someone help me with this one question?

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