Minimize function: Find value of x that result in lowest value of formula

[Gevni]

Hi, I have this formula, What I want is to find the value of "x" so that the result of the formula will be the lowest possible value under the constraint when x !=0, and x<n. Here, values of A,B,C, Q, R,n are already known and fixed.



Can some one please help me to show steps to find the value of x that will minimize this function.

 

[Steven G]

No, sorry. No one here will show you the steps to solve your problem. Rather we will help you figure out the steps to solve your problem. Had you read the forum's guideline you would have know this, supplied us with the work you did and would have received help by now.

So please tell us where you are stuck, where you need help and show us the work you have done so far.

 

[Gevni]

No, sorry. No one here will show you the steps to solve your problem. Rather we will help you figure out the steps to solve your problem. Had you read the forum's guideline you would have know this, supplied us with the work you did and would have received help by now.

So please tell us where you are stuck, where you need help and show us the work you have done so far.

Hi Jomo
So the little bit of background. I am trying to use math in one of the real world optimization problem, in the first step, I generate this formula from a geometrical shape and make it a function of x. Now I have to find lower value of this formula (lower number) based on optimal value of x.I know that x can be between 1 to n-1 . But how do I continue from there? I was thinking there must be a way to calculate it instead of trying a lot of possibilities.

 

[HallsofIvy]

You need to know that the max or min of a differentiable function occurs where the derivative is 0. Do you know how to take the derivative of this function? It appears to be a sum of five relatively simple functions so its derivative is the sum of the derivatives of each.

 

[Gevni]

You need to know that the max or min of a differentiable function occurs where the derivative is 0. Do you know how to take the derivative of this function? It appears to be a sum of five relatively simple functions so its derivative is the sum of the derivatives of each.

Thank you for your reply. I know that I have to take the derivative of this fuction, but I am stuck how to take the derivative of this one as there is no power involve. I tried to simplify it like that,:

 

[Gevni]

Update: I remove the constant n and then take the 1st and 2nd derivative. Now my formula is like that;

[MATH]f(x)=A\left((\frac{Q}{n-x}-\frac{R}{x})+(n-x)\right)+Bx+C(\frac{R}{x})[/MATH]
I took first and 2nd derivative as
[MATH] f′(x)= A\left(\dfrac{R}{x^2}+\dfrac{Q}{\left(n-x\right)^2}-1\right)-\dfrac{CR}{x^2}+B [/MATH]
[MATH] f′′(x)= A(\dfrac{2Q}{(n−x)^3}−\dfrac{2R}{x^3})+\dfrac{2CR}{x^3} [/MATH]
What would be the next step to find value of x that will minimize this equation?