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Is the function f(x) = x^2 - 4x + 4 differentiable at x = 2?

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

Options:

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

Correct Answer: Yes

Solution: 

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

Is the function f(x) = x^2 - 4x + 4 differentiable at x = 2?

Practice Questions

Q1
Is the function f(x) = x^2 - 4x + 4 differentiable at x = 2?
  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 - 4x + 4 differentiable at x = 2?
Correct Answer: Yes
  • Step 1: Identify the function given, which is f(x) = x^2 - 4x + 4.
  • 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 polynomials are smooth and continuous everywhere on the real number line.
  • Step 4: Since the function is a polynomial, it is differentiable at all points, including x = 2.
  • Step 5: Conclude that the function f(x) is differentiable at x = 2.
  • Differentiability of Polynomials – Polynomials are continuous and differentiable everywhere on their domain.
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