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The function f(x) = x^2 - 2x + 1 is differentiable at all points?

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Question: The function f(x) = x^2 - 2x + 1 is differentiable at all points?

Options:

  1. True
  2. False
  3. Only at x = 0
  4. Only for x > 0

Correct Answer: True

Solution: 

f(x) is a polynomial function, which is differentiable everywhere.

The function f(x) = x^2 - 2x + 1 is differentiable at all points?

Practice Questions

Q1
The function f(x) = x^2 - 2x + 1 is differentiable at all points?
  1. True
  2. False
  3. Only at x = 0
  4. Only for x > 0

Questions & Step-by-Step Solutions

The function f(x) = x^2 - 2x + 1 is differentiable at all points?
  • Step 1: Identify the function given, which is f(x) = x^2 - 2x + 1.
  • Step 2: Recognize that this function is a polynomial because it is made up of terms with x raised to whole number powers.
  • Step 3: Understand that polynomial functions are smooth and continuous everywhere on the real number line.
  • Step 4: Conclude that since f(x) is a polynomial, it is differentiable at all points.
  • Differentiability of Polynomial Functions – Polynomial functions are continuous and differentiable at all points in their domain.
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