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

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

Options:

  1. x = 0
  2. x = 1
  3. x = -1
  4. Nowhere

Correct Answer: Nowhere

Solution: 

The function is a polynomial and is differentiable everywhere, hence nowhere.

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

Practice Questions

Q1
Determine the points where f(x) = x^3 - 3x is not differentiable.
  1. x = 0
  2. x = 1
  3. x = -1
  4. Nowhere

Questions & Step-by-Step Solutions

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.
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