For the function f(x) = x^2 - 4x + 4, find the point where it is not differentia

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

Options:

Correct Answer: It is differentiable everywhere

Solution:

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

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

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

Step 1: Identify the function given, which is f(x) = x^2 - 4x + 4.
Step 2: Recognize that this function is a polynomial.
Step 3: Understand that polynomials are smooth and continuous functions.
Step 4: Recall that differentiable means the function has a defined slope at every point.
Step 5: Conclude that since f(x) is a polynomial, it is differentiable everywhere.
Step 6: Specifically, check the point x = 2, which is part of the function.
Step 7: Confirm that f(x) is also differentiable at x = 2.

Differentiability of Polynomials – Polynomials are continuous and differentiable everywhere on their domain.