If f(x) = x^3 - 3x + 2, find f'(1).

If f(x) = x^3 - 3x + 2, find f'(1).

Step 1: Identify the function f(x) = x^3 - 3x + 2.
Step 2: Find the derivative of the function f(x). The derivative f'(x) tells us the rate of change of f(x).
Step 3: Use the power rule to differentiate each term in f(x):
- The derivative of x^3 is 3x^2.
- The derivative of -3x is -3.
- The derivative of the constant 2 is 0.
Step 4: Combine the derivatives to get f'(x) = 3x^2 - 3.
Step 5: Now, we need to find f'(1). This means we will substitute x = 1 into the derivative f'(x).
Step 6: Substitute x = 1 into f'(x): f'(1) = 3(1)^2 - 3.
Step 7: Calculate 3(1)^2, which is 3.
Step 8: Now subtract 3 from 3: 3 - 3 = 0.
Step 9: Therefore, f'(1) = 0.

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