Consider the following maths problem, assuming only a high-school level knowledge of calculus:
If $f(x) = x!$, find $df/dx$
Almost all of my respondents seemed to switch on their "mental differentiation pipeline" and tried to expand $x!$ as a product and got stuck. The right answer is that $x!$ is undefined for any non-integer, so $f$ is discontinuous, and $f'$ doesn't exist!
Is there a name in psychology for the phenomenon that causes one to think along the wrong lines in the problem above?
Is it the same as the one leading to incorrect answers to the bat and ball problem? Is this a test of your thinking style? For, perhaps an intuitive thinking style will lead one to expand $x!$ as a product and attempt to differentiate term-wise. Is there a "cognitive remedy" for wrong thinking?