math challenged
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- May 8, 2020
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Hi guys, to clarify, this is part of an economics problem where I am supposed to find the maximum value of the total revenue function (what level of q (output) total revenue is at its maximum)
So here is the total revenue function (which I have to get the derivative of and set it to 0 to find the maximum value)
TR = [ ((-1/4)q + 75)^1/2 ] * q
It seems that you have to use the chain and product rules to differentiate this, but I'm 100% sure that halfway into the process I'm making some sort of dumb mistake and everything looks like it goes wrong.
So far, I think I found the derivative of the first term using the chain rule. So [ ((-1/4q) + 75)^1/2 ] has a derivative of (-1/8)[ ((-1/4q) + 75)^-1/2 ]. And q has a derivative of 1. I think the product rule says to multiply each function by the derivative of the other function and sum up. So if I am right, the resulting expression from which to obtain the derivative of the TR function would be:
[ ((-1/4)q + 75)^1/2 ] * (1) + (-1/8)[ ((-1/4q)+75)^-1/2 ] * (q)
Evaluating this is where I seem to go horribLy wrong. Or maybe I made a mistake before even reaching this stage, though I don't think I did. Sorry for the long post, any help would be greatly appreciated, thank you!
Just a note: this is not part of a class, just learning this kind of stuff and the calculus that comes with it at my own leisure.
So here is the total revenue function (which I have to get the derivative of and set it to 0 to find the maximum value)
TR = [ ((-1/4)q + 75)^1/2 ] * q
It seems that you have to use the chain and product rules to differentiate this, but I'm 100% sure that halfway into the process I'm making some sort of dumb mistake and everything looks like it goes wrong.
So far, I think I found the derivative of the first term using the chain rule. So [ ((-1/4q) + 75)^1/2 ] has a derivative of (-1/8)[ ((-1/4q) + 75)^-1/2 ]. And q has a derivative of 1. I think the product rule says to multiply each function by the derivative of the other function and sum up. So if I am right, the resulting expression from which to obtain the derivative of the TR function would be:
[ ((-1/4)q + 75)^1/2 ] * (1) + (-1/8)[ ((-1/4q)+75)^-1/2 ] * (q)
Evaluating this is where I seem to go horribLy wrong. Or maybe I made a mistake before even reaching this stage, though I don't think I did. Sorry for the long post, any help would be greatly appreciated, thank you!
Just a note: this is not part of a class, just learning this kind of stuff and the calculus that comes with it at my own leisure.
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