Explanation Given: The sensitivity S to a drug depends on the dosage d in milligrams according to the equation: S = 650 d − 2 d 2 Formula used: The standard form of equation of vertical parabola with its vertex at ( h , k ) is: y = a ( x − h ) 2 + k For the above parabola, if a < 0 then the parabola open downwards and maximum value of the equation occurs at x = h and the maximum value is given as, y = k Calculation: Consider the provided parabolic equation, S = 650 d − 2 d 2 Rewrite the equation as, S = − 2 d 2 + 650 d Form this,

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 9.2, Problem 42E

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To calculate: The maximum sensitivity S to a drug and the dosage d in milligrams that produce the maximum sensitivity.

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Chapter 9.2, Problem 41E

Chapter 9.2, Problem 43E

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In simplest terms, Sketch the graph of the parabola. Then, determine its equation. opens downward, vertex is (- 4, 7), passes through point (0, - 39)

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The maximum sensitivity S to a drug and the dosage d in milligrams that produce the maximum sensitivity.

Solution Summary: The author explains that the maximum sensitivity to a drug depends on the dosage d in milligrams according to the equation.

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Chapter 9 Solutions