All fixed points of function

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Murad Khalilov 2021-1-20

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https://ww2.mathworks.cn/matlabcentral/answers/722578-all-fixed-points-of-function

评论： Rik 2021-1-21

Hello,

how can I find all fixed points of following function: f(x) = cos(x) - 0.07 * x^2. question is so: find all fixed points of this function: f(x)=x.

please, help me, I use roots function but this is not work because I dont know coefficent of cos(x)

Thanks in advance

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Murad Khalilov 2021-1-21

I dont use any code from here, because this is only small part of general task, I only want direction from others, but some codes are not useful for me, this is not fraud, but I dont want that my professor see this post, and also I dont need to show anyone's code as mine, this is not gentle behaviour, also it is not needed to continue this conversation, I only want to delete this forum, if it is not possible, okay, keep so

Rik 2021-1-21

If you are not comitting fraud you should not have anything to worry about.

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回答（2 个）

Walter Roberson 2021-1-20

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syms x

f(x) = cos(x) - 0.07 * x^2;

fplot([f(x)-x,0], [-15 15])

Now you can vpasolve() giving a starting point near a value you read from the graph.

You cannot use roots() for this, as it is not a polynomial.

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Star Strider 2021-1-20

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编辑：Star Strider 2021-1-20

If by ‘fixed points’ you intend ‘roots’, try this:

f = @(x) cos(x) - 0.07 * x.^2;
tv = linspace(-10, 10);
fv = f(tv);
zvi = find(diff(sign(fv)));
for k = 1:numel(zvi)
    idxrng = [max([1 zvi(k)-1]):min([numel(tv) zvi(k)+1])];
    indv = tv(idxrng);
    depv = fv(idxrng);
    B = [indv(:) ones(3,1)] \ depv(:);
    zx(k) = B(2)/B(1);
end
figure
plot(tv, fv, '-b')
hold on
plot(zx, zeros(size(zx)), 'xr')
hold off
grid
legend('Function Value','Roots', 'Location','S')

EDIT —

Added plot image:

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Walter Roberson 2021-1-21

This appears to be a homework question... which is why I chopped out the two exact solutions I was in the middle of posting, and replaced it with a description of strategy instead of complete code.