Question: The function f(x) = x^3 - 3x + 2 is differentiable everywhere. What is f\'(1)?
Options:
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Correct Answer: 0
Solution:
f\'(x) = 3x^2 - 3, thus f\'(1) = 0.
The function f(x) = x^3 - 3x + 2 is differentiable everywhere. What is f'(1)?
Practice Questions
Q1
The function f(x) = x^3 - 3x + 2 is differentiable everywhere. What is f'(1)?
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Questions & Step-by-Step Solutions
The function f(x) = x^3 - 3x + 2 is differentiable everywhere. What is f'(1)?
Step 1: Identify the function given in the question, which is f(x) = x^3 - 3x + 2.
Step 2: To find f'(1), we first need to find the derivative of the function f(x).
Step 3: Use the power rule to differentiate f(x). The derivative of x^3 is 3x^2, and the derivative of -3x is -3. The constant 2 has a derivative of 0.
Step 4: Combine the derivatives to get f'(x) = 3x^2 - 3.
Step 5: Now, substitute x = 1 into the derivative f'(x) to find f'(1).
Step 6: Calculate f'(1) = 3(1)^2 - 3 = 3 - 3 = 0.
Differentiation – Understanding how to find the derivative of a polynomial function.
Evaluation of Derivatives – Calculating the value of the derivative at a specific point.
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