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For the function f(x) = x^2 - 4x + 4, find the point where it is not differentia
For the function f(x) = x^2 - 4x + 4, find the point where it is not differentiable.
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Practice Questions
1 question
Q1
For the function f(x) = x^2 - 4x + 4, find the point where it is not differentiable.
x = 0
x = 2
x = 4
It is differentiable everywhere
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As a polynomial, f(x) is differentiable everywhere, including at x = 2.
Questions & Step-by-step Solutions
1 item
Q
Q: For the function f(x) = x^2 - 4x + 4, find the point where it is not differentiable.
Solution:
As a polynomial, f(x) is differentiable everywhere, including at x = 2.
Steps: 7
Show Steps
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.
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