# How to find the optimal solution between boundary values?

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If a problem a*x+b/x+c

subjected to 0<x<=d

Condition on a,b,c,d such that for optimal solution 0<x*<d?

For example,

x0=0;

f=@(x)(2*x+5/x+10);

x=fmincon(f,x0,[],[],[],[],0,10)

If plotting this,

If I taking the range, 0 to 10 optimal point is 1.581,that is between the boundary

while in the range of 2 to 4,optimal point is 2,that is in the boundary

Also if the range 4 to 10,optimal point is 4,that is in the boundary

So,my problem is to find out at what condition on a,b,c,d such that solution between the boundary not on boundary.

N.B a,b,c,d values are changable.

##### 2 Comments

Bjorn Gustavsson
on 1 Jun 2022

### Accepted Answer

Matt J
on 1 Jun 2022

The derivative of the curve is zero at x=sqrt(b/a). So, the condition is,

0<a,

0<b,

sqrt(b/a)<d

### More Answers (1)

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