Answer: 7
Step-by-step explanation:
To find the absolute minimum we must first take the derivative of the function and find where it equals zero. From there we can use the first derivative test to find where our possible minimum is. We then will test each endpoint and compare for the minimum for this function.
The lowest value is 7. The absolute minimum of this function is 7. If you were to graph it, we'd see that the graph reflects that as well.
Let's start by calling the two numbers we are looking for x and y.
The sum of x and y is 30. In other words, x plus y equals 30 and can be written as equation A:
x + y = 30
The difference between x and y is 20. In other words, x minus y equals 20 and can be written as equation B:
x - y = 20
Now solve equation B for x to get the revised equation B:
x - y = 20
x = 20 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 30
20 + y + y = 30
20 + 2y = 30
2y = 10
y = 5
Now we know y is 5. Which means that we can substitute y for 5 in equation A and solve for x:
x + y = 30
x + 5 = 30
X = 25
Summary: The sum of two numbers is 30 and their difference is 20. What are the two numbers? Answer: 25 and 5 as proven here:
Sum: 25 + 5 = 30
Difference: 25 - 5 = 20
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