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If f(x) = x^2 - 4x + 4, find f'(2).
If f(x) = x^2 - 4x + 4, find f'(2).
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Q1
If f(x) = x^2 - 4x + 4, find f'(2).
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f'(x) = 2x - 4. Thus, f'(2) = 2(2) - 4 = 0.
Questions & Step-by-step Solutions
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Q
Q: If f(x) = x^2 - 4x + 4, find f'(2).
Solution:
f'(x) = 2x - 4. Thus, f'(2) = 2(2) - 4 = 0.
Steps: 6
Show Steps
Step 1: Identify the function f(x) = x^2 - 4x + 4.
Step 2: Find the derivative of the function, which is f'(x).
Step 3: Use the power rule to differentiate: The derivative of x^2 is 2x, and the derivative of -4x is -4.
Step 4: Combine the derivatives: f'(x) = 2x - 4.
Step 5: Now, substitute x = 2 into the derivative: f'(2) = 2(2) - 4.
Step 6: Calculate the result: f'(2) = 4 - 4 = 0.
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