Question

Find two numbers whose difference is 102 and whose product is a minimum. Step 1 If two numbers have a difference of 102, and one of them is x + 102, then the other is $$ Incorrect: Your answer is incorrect. x. Step 2 The product of two numbers x and x + 102 can be simplified to be x2 Correct: Your answer is correct. seenKey 2 + 102 Correct: Your answer is correct. seenKey 102 x. Step 3 If f(x) = x2 + 102x, then f '(x) = $$ Correct: Your answer is correct. 2x+102. Step 4 To minimize the product f(x) = x2 + 102x, we must solve 0 = f '(x) = 2x + 102, which means x = -51 Correct: Your answer is correct. seenKey -51 . Step 5 Since f ''(x) = 2 , there must be an absolute minimum at x = −51. Thus, the two numbers are as follows. (smaller number) (larger number)

Answer 1

Answer:

The two numbers would be -51 and 51

Step-by-step explanation:

To find these, first set the equation for the first number as x. You can then set the second number as x + 102. Now, find their product.

x(x + 102) = x^2 + 102x

Now, to find the minimum, find the value of x in the vertex of this equation.

-b/2a = -102/2(1) = -102/2 = -51

So we know -51 is the first number. Now we find the second using the prewritten equation.

x + 102 = -51 + 102 = 51