Find two numbers whose difference is 176 and whose product is a minimum.

1 answer:

8 0

Let the two required numbers be x and y, then x - y = 176, thus y = x - 176.

Let the product of the two numbers be represented by

$P = xy x(x - 176) = x^2 - 176x$

For the product to be minimum, $\frac{dP}{dx} =0$

$\frac{dP}{dx} =2x - 176=0 \\ \\ \Rightarrow2x=176 \\ \\ \Rightarrow x=88$

Thus, y = 88 - 176 = -88

Therefore, the two numbers are 88 and -88.

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If g(x) = 4√x-8 , which statement is true?

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$g(x)=4\sqrt{x}-8$

So if we graph this function we will get the Figure below. Thus, let's study both the equation and the graph to get some conclusions. Therefore, we can assure these statements:

First. The function is defined only for $x\geq 0$ as shown in the Figure. This is also true because of $\sqrt{x}$ where $x$ must be greater (or equal) than zero.

Second. The range of the function are the values of $y\geq -8$ .

Third. If $x$ creases then $y$ always creases, too.