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Reviewed CSCA Mathematics question · Hard

For the function f(x) = 2x^3 - 9x^2 + 12x - 5, what is the slope of the tangent line at x = 1?

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

Correct answer

A. 0

Principle or equation

The slope of the tangent line to f at x = a is f'(a). Use power rule for differentiation.

Why this answer is correct

f'(x) = 6x^2 - 18x + 12. Evaluate at x = 1: f'(1) = 6(1)^2 - 18(1) + 12 = 6 - 18 + 12 = 0.

Example

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

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