disp('Solutions for f''''(x) = 0:');
disp("Solutions for f''(x) = 0:");
That is, inside a ' ' (apostrophe) delimited character vector, a single ' ends the character vector and '' (two ' in a row) results in a single ' in the character vector.
Inside a " " (double-quote) delimited character vector, each ' is literal, just a plain character -- but a single " (double-quote) ends the string and "" (two double-quote in a row) results a single " in the string.