# Finding full graph / minimum without an x range

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Ashley Sullivan on 29 Mar 2020
Edited: dpb on 30 Mar 2020
I am plotting a function and looking for its minimum, but the only parameter for the x value that I'm given is that it needs to be in increments of 1. I can also infer from the problem that the x must be positive.
Is there a function to make a "fit" of the graph without knowing an explicit x range? Right now, my method is to just guess for x variables until I get something that looks right, but I'd rather not do it that way.
Mohammad Sami on 30 Mar 2020
Edited: Mohammad Sami on 30 Mar 2020
y = @(x)0.04.*x.^2 + 0.3.*(16100./x).^2;
fplot(y);
fplot(y,[1 1000]); % to plot a range

dpb on 30 Mar 2020
Edited: dpb on 30 Mar 2020
Well, with such disparate magnitudes in terms, the interesting part is somewhat harder to envision...the second part goes to +inf @ origin while --> 0 as x-->inf so quadratic doesn't have any real counter effect until x gets large enough that the inverse x^2 term begins to go away...
To try to do something automagically to bound, I'd probably try something like
>> fnz=@(x) 0.04*x.^2 - 0.3*(16100./x).^2
fnz =
function_handle with value:
@(x)0.04*x.^2-0.3*(16100./x).^2
>> x0=fsolve(fnz,100)
Equation solved.
fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.
<stopping criteria details>
x0 =
209.9802
>> xl=10.^fix(log10(z0)+[-1 1]);
>> yl=10.^fix(log10(z0)+[ 0 1]);
>> fplot(y,xl) % using Mohammed's function definition above here...
>> xlim(xl), ylim(yl)
>> hAx=gca;
>> hAx.XScale='log';
>> hAx.YScale='log';
>> grid on
produced