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Question

The function p, where p(x)=−x2+14x−40, models the profit from Lindsey's store, in thousands of dollars, after x months of opening the store.

Part A

Based on the function, when did Lindsey's store have a profit of zero dollars?

Enter your answers in the empty boxes to correctly complete the sentence.

The store had $0 profit first in month and then in month .

Part B

When did the store have its maximum profit, and what was the profit?

Enter your answers in the empty boxes to correctly complete the sentence.

The maximum profit of $ occurred in month .

Answer 1

p(x)=0=x²-14x+40 (multiply by -1!)

(x-10)(x-4)=0...so no profit in months 4 and 10.

Set the derivative pof p(x) to zero: -2x+14=0.

Max profit in month 7.

You plug in 7 to the function to get the max profit..