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