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Is the function f(x) = x^2 - 4x + 4 differentiable at x = 2?
Is the function f(x) = x^2 - 4x + 4 differentiable at x = 2?
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Practice Questions
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Q1
Is the function f(x) = x^2 - 4x + 4 differentiable at x = 2?
Yes
No
Only from the left
Only from the right
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The function is a polynomial and is differentiable everywhere, hence yes.
Questions & Step-by-step Solutions
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Q
Q: Is the function f(x) = x^2 - 4x + 4 differentiable at x = 2?
Solution:
The function is a polynomial and is differentiable everywhere, hence yes.
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 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.
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