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For the function f(x) = x^3 - 3x^2 + 4, find the points where it is not differen

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Question: For the function f(x) = x^3 - 3x^2 + 4, find the points where it is not differentiable.

Options:

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

Correct Answer: None

Solution: 

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

For the function f(x) = x^3 - 3x^2 + 4, find the points where it is not differen

Practice Questions

Q1
For the function f(x) = x^3 - 3x^2 + 4, find the points where it is not differentiable.
  1. None
  2. x = 0
  3. x = 1
  4. x = 2

Questions & Step-by-Step Solutions

For the function f(x) = x^3 - 3x^2 + 4, find the points where it is not differentiable.
  • Step 1: Identify the function given, which is f(x) = x^3 - 3x^2 + 4.
  • 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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