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Find two numbers whose sum is 22 and whose product is the maximum possible value...

A) Quadratic equation
B) Optimization problem
C) Linear algebra
D) Arithmetic progression

User Johnchase
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1 Answer

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Final answer:

To find two numbers whose sum is 22 and whose product is the maximum possible value, we can use optimization techniques by setting up a quadratic equation and finding the critical points. The answer is option B) Optimization problem.

Step-by-step explanation:

To find two numbers whose sum is 22 and whose product is the maximum possible value, we can use optimization techniques. Let's call the two numbers x and 22 - x, where x is the first number. The product of these two numbers is given by P = x(22 - x), which is a quadratic equation.

To find the maximum value of P, we can use calculus. Taking the derivative of P with respect to x and setting it equal to zero, we can find the critical points which correspond to the maximum value of P. Solving for x, we get the value of x at which the product is maximized. Plugging this value back into the equation, we can find the second number.

Therefore, the answer is option B) Optimization problem.

User Curlew
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