Finding Numbers In Exercises 5-10, find two positive numbers that satisfy the given requirements.
The product is 185 and the sum is a minimum.
To calculate: The two positive numbers that under the conditions “Product of the two is 185” gives the minimum sum.
The product of the two is 185.
For a function f that is twice differentiable on an open interval I, if for some c, then,
If the function f has relative minima at c if the function f has relative maxima at c. If , the test fails.
Consider the two numbers to be x and y.
Then the quantity to be minimized or the primary equation is:
Now, the product of the two numbers is 185. This gives:
Substitute this back in the primary equation to obtain:
Differentiate this and equate it to zero to obtain,
As the numbers are positive, the negative one is discarded
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