Math Notes

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Differential Calculus Solutions

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The sum of two numbers is 15. What are these numbers if their product is as large as possible.

Let x, y be the numbers

Thus x + y = 15

x y = p(Their product)

$$P = x(15-x)$$

$$P = 15x-x^2$$

$$\frac{dP}{dx} = 15-2x$$

$$0 = 15-2x$$

$$x = 7.5$$

$$y = 7.5$$

Thus the numbers are:

$$x = 7.5$$

$$y = 7.5$$