For the function f(x) = x^3 - 5x^2 + 3x - 2, what is the slope of the tangent line at x = 2?
Show the answer and explanation
Correct answer
A. -5
Principle or equation
The slope of the tangent line at a point is given by the derivative of the function evaluated at that point.
Why this answer is correct
f'(x) = 3x^2 - 10x + 3. Evaluating at x = 2: f'(2) = 3(4) - 10(2) + 3 = 12 - 20 + 3 = -5.
Example
For f(x) = x^2, f'(x) = 2x, so slope at x = 3 is 6.
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