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The function f(x) = x^2 - 4x + 4 is differentiable at x = 2?

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Question: The function f(x) = x^2 - 4x + 4 is differentiable at x = 2?

Options:

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

Correct Answer: Yes

Solution: 

f(x) is a polynomial function, hence differentiable everywhere including at x = 2.

The function f(x) = x^2 - 4x + 4 is differentiable at x = 2?

Practice Questions

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

Questions & Step-by-Step Solutions

The function f(x) = x^2 - 4x + 4 is differentiable at x = 2?
  • Step 1: Identify the function given, which is f(x) = x^2 - 4x + 4.
  • Step 2: Recognize that this function is a polynomial function.
  • Step 3: Understand that polynomial functions are smooth and continuous everywhere.
  • Step 4: Conclude that since f(x) is a polynomial, it is differentiable at all points, including at x = 2.
  • Differentiability of Polynomial Functions – Polynomial functions are differentiable everywhere on their domain, which includes all real numbers.
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