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Reviewed CSCA Mathematics question · Hard

For the function f(x) = 2x^3 - 3x^2 - 12x + 5, what is the slope of the tangent line at x = 1?

  1. -12
  2. -6
  3. 0
  4. 6
Show the answer and explanation

Correct answer

A. -12

Principle or equation

The slope of the tangent line at a point is the derivative evaluated at that point.

Why this answer is correct

Compute f'(x) = 6x^2 - 6x - 12. Evaluate at x = 1: f'(1) = 6(1)^2 - 6(1) - 12 = 6 - 6 - 12 = -12.

Example

For f(x) = x^3 - 2x, f'(x) = 3x^2 - 2, so at x = 2, slope = 10.

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