Question

Find two numbers whose sum is 45 and whose product is a maximum. (If an answer does not exist, enter DNE.)

smaller number:

larger number:

Answer 1

Let, one be x and therefore the another number be 45-x. Define the product function, P(x)= x(45-x). Then, by finding the critical point of P(x) and applying the second derivative test, we have got the numbers.