= x^3 + x^2 + 3*x + 4; would require that x already been given a definite value, and it would calculate f as being a particular numeric value. The x would have to be a numeric scalar or a square two-dimensional array for that code to work. For example if x = 3 before that, then f would be assigned the single scalar value 49. You then pass that numeric f into the routine that tries to access the numeric array as a function, and that of course fails.
= @(x) x^3 + x^2 + 3*x + 4; would define a rule, that f is to be a function that expects a single argument that for the purposes of the call will be known as x. For any one call, the x that is passed in to the function is to have the formula applied to it and the result returned. If a different argument is provided then a different result would be calculated.
= @(x) x^3 + x^2 + 3*x + 4; is mostly equivalent to having written
function r = f(x)
r = x^3 + x^2 + 3*x + 4;
end
but does have some subtle differences not worth discussing at the moment.
