Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.
Correct Answer: Yes, f(x) is differentiable at x = 1.
- Step 1: Identify the function given, which is f(x) = x^3 - 3x + 2.
- Step 2: Recognize that f(x) is a polynomial function.
- Step 3: Understand that polynomial functions are smooth and continuous everywhere.
- Step 4: Conclude that since f(x) is a polynomial, it is differentiable at all points, including x = 1.
- Differentiability of Polynomial Functions – Polynomial functions are continuous and differentiable at all points in their domain.
