Posted by admin | Posted in Bestsellers | Posted on 06-09-2008
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I need help with a math question adn tell me how to do it step pby step?
The daily profit P(in thousands of dollars)from the sale of textbooks is a function of the number of x textbooks sold(in hundreds). The formula for the function is P= -3xsquared + 12x – 4.
What sales amount results in the maxium daily profit ? What is the maxium daily profit?
sales amount = _ textbooks
maxium daily profit=_dollars
P = -3x^2 + 12x – 4
This function is an upside-down parabola since the coefficient of the x^2 term is negative. (Recall that all parabolas have the form f(x) = ax^2 + bx + c).
The maximum daily profit will occur at the top of the inverted parabola (the vertex). To find out where it is, take the derivative of P to find the tangent line to the curve where the slope = 0.
P’ = -6x + 12 = 0
x = 2 (200 textbooks sold) is where the parabola is at its maximum.
The daily profit there is
P(2) = -3((2)^2) + 12(2) – 4 = 8 (thousand dollars)
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