The product of two numbers is 32. find the sum of the two numbers s(x) as a function of one of the numbers, x. s(x) = find the positive numbers that minimize the sum and list them in increasing order: (smaller number) = ? (larger number) = ? let c be the smaller of the two numbers that minimize the sum. then c = ? s'(c) = ? and s"(c) = ?

Step-by-step explanation:

We are given the following information in the question:

The product of two numbers is 32.

Let the two numbers be x and y, then,

The sum of the two numbers = S(x)

First, we differentiate S(x) with respect to x, to get,

Equating the first derivative to zero, we get,

Solving, we get,

Again differentiation S(x), with respect to x, we get,

At,

Thus, minima occurs at x = for S(x).

If c be the smaller of the two numbers that minimize the sum, then,

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40