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Reviewed CSCA Mathematics question · Hard

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

  1. -3
  2. 3
  3. 9
  4. 0
Show the answer and explanation

Correct answer

A. -3

Principle or equation

The slope of the tangent line to y = f(x) at x = a is f'(a). For a polynomial, differentiate term by term.

Why this answer is correct

f'(x) = 3x^2 - 12x + 9. At x = 2, f'(2) = 3(4) - 12(2) + 9 = 12 - 24 + 9 = -3.

Example

For f(x) = x^2 - 4x + 3, f'(x) = 2x - 4, so at x = 3, slope = 2.

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