For the function f(x) = x^3 - 3x^2 + 2, what is the slope of the tangent line at x = 2?
Show the answer and explanation
Correct answer
A. 0
Principle or equation
The slope of the tangent line at a point is the derivative evaluated at that point. For f(x) = x^n, derivative is n x^(n-1).
Why this answer is correct
f'(x) = 3x^2 - 6x. At x=2, f'(2) = 3(4) - 6(2) = 12 - 12 = 0.
Example
For f(x)=x^2, f'(3)=6, so slope at x=3 is 6.
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