How to choose two numbers for which the sum of their square roots is minimal, knowing that the product of the two numbers is #a#?
How can I solve the problem with derivatives?
How can I solve the problem with derivatives?
3 Answers
Explanation:
I'll try to take you through the solution method below.
Explanation:
What are we looking for?
Two numbers. Let's give them names,
#x# and#y# .
Reread the question.
We want to make the sum of the square roots minimal.
This tells us two things
(1) both numbers are non-negative (to avoid imaginaries)
(2) We are interested in the value of#sqrtx+sqrty#
Reread the question.
We also are told that the product of
Who chooses
In general, if an exercise says something about
So we might be told "the product of
or "the product of
We are to solve all of these at once by saying
So, we want to make
This looks like an optimization problem and it is one. So I want a function of one variable to minimize.
So
Now we want to minimize:
Find the derivative, then the critical number(s) and test the critical number(s). Finish be finding
Critical
Explanation:
We know that for
then
but