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Is the function f(x) = x^2 - 2x + 1 differentiable at x = 1?

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Question: Is the function f(x) = x^2 - 2x + 1 differentiable at x = 1?

Options:

  1. Yes
  2. No
  3. Only from the left
  4. Only from the right

Correct Answer: Yes

Solution: 

f(x) is a polynomial function, which is differentiable everywhere, including at x = 1.

Is the function f(x) = x^2 - 2x + 1 differentiable at x = 1?

Practice Questions

Q1
Is the function f(x) = x^2 - 2x + 1 differentiable at x = 1?
  1. Yes
  2. No
  3. Only from the left
  4. Only from the right

Questions & Step-by-Step Solutions

Is the function f(x) = x^2 - 2x + 1 differentiable at x = 1?
Correct Answer: Yes, f(x) is differentiable at x = 1.
  • Step 1: Identify the function f(x) = x^2 - 2x + 1.
  • Step 2: Recognize that this function is a polynomial.
  • Step 3: Understand that polynomial functions are smooth and continuous.
  • Step 4: Know that smooth and continuous functions are differentiable everywhere.
  • Step 5: Conclude that since f(x) is a polynomial, it is differentiable at x = 1.
  • Differentiability of Polynomial Functions – Polynomial functions are continuous and differentiable at all points in their domain.
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