How do I make this command to get the result correctly? Please help me to solve this..

I have two functions. for example,

f(x) = 3x^2-2y+5 (plot for x>1);
g(x) = 4x^3-3x-7;

For f(x), x is variable and y is a arbitrary fixed number. So, by choosing arbitrary 'y', I can have many graphs for f(x) (for instance: if 'y=2' then I can have one graph for f(x), and for 'y= 2.01' I will have other graph and so on). And For g(x), x is a variable. So, I will get only one graph for g(x) for non-negative x.

My goal is to find an unique intersection point 'x_0' between g(x) and f(x) such that,

 g(x_0) = c(constant) + minimum(f(x)).

here I can change y arbitrarily in f(x), to get my correct 'x_0'. So, I might need to do iteration here. But I don't know how to write this command. Please help me. Thank you for your time.

N.B.:I posted this question couple of days before and there was some typos, that is why I asking again with corrections.

[Stephen23]

Original question:

https://www.mathworks.com/matlabcentral/answers/421300-can-somebody-help-me-please-to-write-the-code-to-fulfill-this-condition-in-matlab

Answer 1

[Dimitris Kalogiros]

If you have license for symbolic math toolbox, try this :

close all
clearvars

syms x y

   f(x)=3*x^2-2*y+5

   g(x)=4*x^3-3*x-7

   figure;
   fplot(g(x), [0 3]); hold on;
   for yval=-5:1:5
       f1(x)=subs(f(x),y,yval);
       fplot(f1(x),[0,3]);
   end

   grid on; zoom on;

Results, should be something like this:

[Md Abu Helal]

@ Dimitris, Thank you for your time. I would like to know, how do I get the numerical value of intersection point from the graph? In other words, what command should I put here to identify intersection point(x_0 value) and minimum of f(x). That will be all for me. Thank you again and looking for your help.

[Dimitris Kalogiros]

Try this:

close all
clearvars

syms x y;

f(x)=3*x^2-2*y+5
g(x)=4*x^3-3*x-7

figure;
fplot(g(x), [0 3]); hold on;
for yval=-5:1:5
    f1(x)=subs(f(x),y,yval);
    fplot(f1(x),[0,3]);
    assume(x, 'real')
    x_0=vpasolve(g(x)==f1(x), x, [0, inf])

end
grid on; zoom on;

[Md Abu Helal]

@ Dimitris,Thank you so much