For the function f(x) = 2x^3 - 3x^2 - 12x + 7, 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 x-value.
Why this answer is correct
f'(x) = 6x^2 - 6x - 12. At x = 2, f'(2) = 6(4) - 6(2) - 12 = 24 - 12 - 12 = 0. So the slope is 0.
Example
For f(x) = x^3 - 4x, f'(x) = 3x^2 - 4, so slope at x=1 is -1.
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