7.) the growth rate y (in pounds per month) of an infant is related to present weight x (in pounds) by the…

7.) the growth rate y (in pounds per month) of an infant is related to present weight x (in pounds) by the formula y = cx(21 - x), where c is a positive constant and 0 < x < 21. at what weight does the maximum growth rate occur?

7.) the growth rate y (in pounds per month) of an infant is related to present weight x (in pounds) by the formula y = cx(21 - x), where c is a positive constant and 0 < x < 21. at what weight does the maximum growth rate occur?

Answer

Explanation:

Step1: Expand the function

$y = cx(21 - x)=21cx - cx^{2}$.

Step2: Take the derivative

The derivative $y'$ of $y = 21cx - cx^{2}$ with respect to $x$ is $y'=21c - 2cx$.

Step3: Set the derivative equal to zero

Set $y' = 0$, so $21c - 2cx=0$.

Step4: Solve for $x$

Factor out $c$ (since $c>0$) to get $c(21 - 2x)=0$. Then $21 - 2x = 0$, and $x=\frac{21}{2}=10.5$.

Answer:

$10.5$ pounds