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