Stanton D. answered • 02/10/21
Tutor to Pique Your Sciences Interest
So Emma B., How do you solve a word problem in a math course? You turn it into a math equation, as I hope you know by now.
So, call the smaller of the two numbers x . What is the other number, if the product of the two numbers is 152? You had better be able to do this in your head: (152/x)*(x) = 152, right? So, 152/x .
Now for the fun part. What is the constraint in the problem? The sum of the two numbers is a minimum.
So, call the sum of the two numbers S . What do you know, beyond any shadow of a doubt, about the graph of S vs. x ? From the statement of the problem, you know there is going to be a minimum. And what is true about a function at the point at which it has a minimum? Now it's time for a little calculus!
You had better be able to say, the first derivative has a value of zero.
And how do you go about taking the first derivative of the function S (x) = x + (152/x) ?
I'll leave the rest up to you. You will come up with a value near 12.3, but you will NOT express it as a decimal value, I hope (Just sayin').
-- Cheers, -- Mr. d.
Stanton D.
Technically, you should check that you have a minimum, by taking S '' (x), or alternatively by testing values to either "side" of this. Since you have a pretty simple function, with only a single S' (x)= 0 spot, you would get by with a single test value (rationale: if the spot you found were a maximum, your sidewards test value would give a lower sum. But it doesn't, so it must be a minimum).02/10/21