Answer:
-100
-10, 10
Step-by-step explanation:
Let the smaller number be x.
Then the larger number is x + 20.
The product is x(x + 20).
Now you can write the function
y = x(x + 20)
y = x^2 + 20x
Take the first derivative of y with respect to x.
y' = 2x + 20
Set the first derivative equal to zero to find the x value for the minimum value of the function.
2x + 20 = 0
2x = -20
x = -10
The minimum value of the function occurs at x = -10. -10 is one of the two numbers.
y = x^2 + 20x
For x = -10,
y = (-10)^2 + 20(-10)
y = 100 - 200
y = -100
The minimum value of the product is -100.
x = -10
x + 20 = -10 + 20 = 10
The numbers are -10 and 10.
If you have not learned derivatives yet, then plot the function
y = x^2 + 20x
Now look at the graph and find the minimum y value and the x value at which it occurs.
The minimum y value is -100. That is the minimum product you are looking for.
The x value of the minimum function value is x = -10.
Then x + 20 = -10 + 20 = 10.
The numbers are -10 and 10.
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