Storing and comparing values of an equation in loop

I'm trying to run an equation f(x) for different values of x. Then I'll comapre the outputs for different values of x and return the value of x for which f(x) is maximum.

Here is the code:

i=1;

for x = 0 : 0.1 : 1

f(i) = x * exp((-2)*(x));

i= i+1;

if f(i) > f(i-1) && f(i) < f(i+1)

continue;

else

disp(x);

break;

end

end

I know there are many mistakes but this is how I imagine the code to work. Apologies for any newbie mistakes since I am an absolute begineer. Please help me.

Answer 1

[VBBV]

syms x f(x)
f = x*exp(-2*x)

f = 

F = diff(f,x) == 0

F = 

X = 0 : 0.1 : 1; 
idx = find(double(subs(F,x,X)))

idx = 6

Max = X(idx)

Max = 0.5000

plot(X,double(subs(f,x,X)))

Answer 2

[Voss]

I think this is what you're going for. Note that it's not convenient to calculate each f(i) inside the loop, because you'll need f(i+1) as well, in order to check whether f(i) is a local maximum. So you can calculate all f before the loop.

% define x
x = 0 : 0.1 : 1;

% calculate f at all x values
f = x .* exp(-2*x);

% iterate over the elements of x and f that have one before and one after
% (that is, exclude the first and last elements)
for i = 2:numel(x)-1
    
    % local maximum condition: f(i) is greater than both f(i-1) and f(i+1)
    if f(i) > f(i-1) && f(i) > f(i+1)
        disp(x(i));
        break;
    end
    
end

    0.5000

% a plot for verification/visualization
plot(x,f)
hold on
plot(x(i),f(i),'ro')