Step 1: Identify the function f(x) = x^3 - 3x^2 + 4.
Step 2: Find the derivative of the function, denoted as f'(x).
Step 3: Use the power rule to differentiate each term: The derivative of x^3 is 3x^2, the derivative of -3x^2 is -6x, and the derivative of the constant 4 is 0.
Step 4: Combine the derivatives to get f'(x) = 3x^2 - 6x.
Step 5: Substitute x = 1 into the derivative: f'(1) = 3(1)^2 - 6(1).
Step 6: Calculate 3(1)^2 which equals 3, and calculate -6(1) which equals -6.
Step 7: Combine the results: 3 - 6 = -3.
Step 8: Conclude that f'(1) is equal to -3.
Differentiation – The process of finding the derivative of a function, which represents the rate of change of the function with respect to its variable.
Evaluation of Derivatives – Substituting a specific value into the derivative function to find the slope of the tangent line at that point.
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