Determine the points where f(x) = x^3 - 3x is not differentiable.
Correct Answer: f(x) = x^3 - 3x is differentiable everywhere.
- Step 1: Identify the function given, which is f(x) = x^3 - 3x.
- Step 2: Recognize that this function is a polynomial.
- Step 3: Understand that polynomials are smooth and continuous everywhere on the real number line.
- Step 4: Conclude that since the function is a polynomial, it is differentiable at all points.
- Step 5: Therefore, there are no points where the function is not differentiable.
- Differentiability of Polynomials – Polynomials are differentiable everywhere on their domain, which is all real numbers.
