For the function f(x) = x^3 - 6x^2 + 9x + 1, what is the slope of the tangent line at x = 1?
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Correct answer
A. 0
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
f'(x) = 3x^2 - 12x + 9. At x = 1, f'(1) = 3(1)^2 - 12(1) + 9 = 3 - 12 + 9 = 0.
Example
For f(x) = x^2, f'(2) = 2*2 = 4.
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