Final answer:
The function f(x) = x¹¹ is a polynomial, which is differentiable for all x-values where x is a real number, without any restrictions.
Step-by-step explanation:
The student asked to describe the x-values at which the function f(x) = x¹¹ is differentiable. The function f(x) = x¹¹ is a polynomial, and polynomial functions are differentiable everywhere on the real number line. This means that f(x) is differentiable for all real numbers, and there are no restrictions on the x-values for the differentiability of this function. Polynomials are smooth and continuous functions, and their derivatives exist at every point in their domain. Therefore, for the function f(x) = x¹¹, it is differentiable for all x-values where x is a real number.