How to find the optimal solution between boundary values?

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)

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

x = 1.5811

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.

[Bjorn Gustavsson]

Start by familiarize yourself with the problem. By that I mean plot the curves (positive x only it seems?) for a range of a, b and c values just to see how the curve varies. That should take you a long way towards solving this problem.

[ancy s george]

ok sir,Thank you

Answer 1

[Matt J]

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

0<a,
0<b,
sqrt(b/a)<d

[ancy s george]

Thank you

Answer 2

[M Mirrashid]

https://ch.mathworks.com/matlabcentral/fileexchange/112600-transit-search-optimization-algorithm-matlab-codes