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Reviewed CSCA Mathematics question · Standard

For the function f(x) = x^3 - 6x^2 + 9x + 2, what is the slope of the tangent line at x = 1?

  1. 0
  2. 6
  3. -6
  4. 3
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. f'(x) = 3x^2 - 12x + 9.

Why this answer is correct

f'(x) = 3x^2 - 12x + 9. At x = 1, f'(1) = 3 - 12 + 9 = 0.

Example

For f(x) = x^2, f'(x) = 2x, so slope at x = 3 is 6.

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