The positive numbers x and a−x have a sum of a. What is x in terms of a if the product x⋅(a−x) is a maximum?Choose 1 answer:(A) 2a(B) 2a(C) a(D) a(E) There is no x that would produce a maximum product
Q. The positive numbers x and a−x have a sum of a. What is x in terms of a if the product x⋅(a−x) is a maximum?Choose 1 answer:(A) 2a(B) 2a(C) a(D) a(E) There is no x that would produce a maximum product
Equation Simplification: We know that x+(a−x)=a. This simplifies to x+a−x=a, which means x cancels out and we're left with a=a, which is true but doesn't help us find x.
Maximizing Product: To maximize the product x(a−x), we can use the fact that for a fixed sum, the product of two numbers is maximized when the numbers are equal. So, we set x=a−x.
Solving for x: Solving for x gives us x=a−x, which simplifies to 2x=a.
Isolating x: Divide both sides by 2 to isolate x, we get x=2a.
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