Running a while loop one time after the parameter is met

The problem is to write a code that will approximate the slope of an equation at a point by using the value of the function at a point x and a point xi. The slope is being approximated by using f(xi)-f(x)/xi-x. X is randomly generated, and the increment between the points x and xi is to be 1 at first, and to be halved each loop until two consecutive slope approximations are within 1% of each other. My issue is that I got the code to loop until f(xi) is within 1% of f(x), but I don't know how to phrase my condition or nest another statement to get the loop to run one more time to satisfy the requirement of two consecutive approximations being within 1% of each other. I "manually" ran the sequence one more time after the while loop to obtain the correct answer, but I know that I should be able to do it within a single loop.

x=rand*9+1;
n=1; % increment
xi=x+n;
y=(5*x^2)/(log10(7*x^4)); % function to approximate slope of
yi=(5*xi^2)/(log10(7*xi^4));
while ((yi-y)/y)>0.01
    n=n/2;
    xi=x+n;
    yi=(5*xi^2)/(log10(7*xi^4));
end
n=n/2;
xi=x+n;
yi=(5*xi^2)/(log10(7*xi^4));
slope=(yi-y)/(xi-x)

[Askic V]

Hello Logan,

please have a look at this thread:

https://www.mathworks.com/matlabcentral/answers/115403-do-while-loop-in-matlab

Basically you need this:

while true
    n=n/2;
    xi=x+n;
    yi=(5*xi^2)/(log10(7*xi^4));
    if (yi-y)/y<=0.01
        break
    end
end

Answer 1

[Aditya Srikar]

Hi Logan

The condition in while loop need to be

(yi-y)/y<=0.01

Modify the condition and the code should work fine.

I hope this helps