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Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?
Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?
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Practice Questions
1 question
Q1
Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?
Yes
No
Only at x = 0
Only at x = 2
Show Solution
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This is a polynomial function, which is differentiable everywhere on its domain.
Questions & Step-by-step Solutions
1 item
Q
Q: Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?
Solution:
This is a polynomial function, which is differentiable everywhere on its domain.
Steps: 5
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 function.
Step 3: Understand that polynomial functions are smooth and continuous.
Step 4: Know that smooth and continuous functions are differentiable everywhere on their domain.
Step 5: Conclude that since f(x) is a polynomial, it is differentiable everywhere.
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