Here's the problem:
The growth rate y (in pounds per month) of infants is related to their present weight x (in pounds) by the formula y=cx(21-x) for some constant c>0. At what weight is the rate of growth a maximum.

It says I need to use the -b/2a formula, but I'm not sure how to use that formula with this problem. Can anyone help point me in the right direction?

Thanks,
-M.

Distribute the cx(21 - x) to put it in polynomial form. The 'b' is then the coefficient in front of the 'x' term and the 'a' is the coefficient in front of the 'x^2' term. Calculate the specific value of -b/2a.

Quote:

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Originally Posted by s_cianci

Distribute the cx(21 - x) to put it in polynomial form. The 'b' is then the coefficient in front of the 'x' term and the 'a' is the coefficient in front of the 'x^2' term. Calculate the specific value of -b/2a.

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While this gives you the location of a vertex, it does not tell you if that vertex is a maximum or a minimum. We need to take it one step further.

Lets follow s_cianci's instructions and distribute cx



The general form for a polynomial is

if your going to use the form

This part may get a little confusing, the c in your equation is not the same as the one in the general form.

your a=-c and b=21c because those are the coefficients in front of the and x

Now depending on your instructor you may or may not have to do the maximum test below, but you do have to somehow prove it's a maximum, it's part of the question. If saying the coefficient is negative is sufficient then I would just stick with that!

Now test values just to the left of and values just to the right of . If both values just to the left of and to the right of are both less than , then we have a maximum.:D

Thank you s_cianci and Nhatkiem! =)