1. Let's clarify the problem: We want to understand when the gradient (slope) of a function is undefined. 2. The gradient of a function at a point is undefined when the derivative does not exist at that point. 3. For example, the gradient is undefined if the function has a vertical tangent line at that point. 4. Being a whole number for $x$ alone does not guarantee the gradient is undefined; it depends on the function's behavior at that $x$. 5. For instance, for the function $f(x) = \frac{1}{x}$, the gradient is undefined at $x=0$ because the function is not defined there. 6. If you have a specific function, we can find where its derivative is undefined by checking points where the derivative formula involves division by zero or other discontinuities. 7. In summary, the gradient is undefined at points where the derivative does not exist, not simply because $x$ is a whole number.