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)

Question

Ali

Mathematics

18 May, 20:42

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)

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Answers (1)

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Jazlene Burton · Answer 1

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