Mathematics, 17.07.2019 23:00 bfer11
The sum of two integers is 16. find the values of these two integers so that their product is a maximum, and find the maximum value of the product.
Answers: 1
![f(x)=-x^2+16x=-(x^2-16x)=-(x^2-2\cdot x\cdot8)\\\\=-(\underbrace{x^2-2\cdot x\cdot8+8^2}_{(a-b)^2=a^2-2ab+b^2}-8^2)=-[(x-8)^2-64]\\\\=-(x-8)^2+64\\\\h=8\ \text{and the maximum is equal 64} \\\\\text{The integers}\\x=8;\ y=16-8=8\\\\\text{The maximum is equal}\ 64](/tpl/images/0101/8506/6363e.png)
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The sum of two integers is 16. find the values of these two integers so that their product is a maxi...
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