For the function f(x) = x^3 - 3x^2 + 2, what is the slope of the tangent line at x = 1?
Show the answer and explanation
Correct answer
A. -3
Principle or equation
The slope of the tangent line to a function at a point is given by the derivative evaluated at that point.
Why this answer is correct
First find the derivative: f'(x) = 3x^2 - 6x. Then evaluate at x = 1: f'(1) = 3(1)^2 - 6(1) = 3 - 6 = -3.
Example
If f(x) = x^2, then f'(x) = 2x and the slope at x = 3 is 6.
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