For the function f(x) = x^3 - 4x^2 + 2x - 1, what is the slope of the tangent line at x = 2?
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Correct answer
A. -2
Principle or equation
The slope of the tangent line at a point is the derivative of the function evaluated at that point.
Why this answer is correct
Find f'(x) = 3x^2 - 8x + 2. Evaluate at x = 2: f'(2) = 3(4) - 8(2) + 2 = 12 - 16 + 2 = -2.
Example
For f(x) = x^2, f'(x) = 2x, so slope at x=3 is 6.
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