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Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.

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Question: Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.

Options:

  1. x = 0
  2. x = 1
  3. x = 2
  4. None

Correct Answer: None

Solution: 

The function is a polynomial and is differentiable everywhere. Thus, there are no points where it is not differentiable.

Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.

Practice Questions

Q1
Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.
  1. x = 0
  2. x = 1
  3. x = 2
  4. None

Questions & Step-by-Step Solutions

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.
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