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Reviewed CSCA Mathematics question · Standard

For the function f(x) = x^3 - 6x^2 + 11x - 6, what is the slope of the tangent line at x = 2?

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

Correct answer

A. -1

Principle or equation

The slope of the tangent line to f at x = a is f'(a). For a polynomial, differentiate term by term: d/dx(x^n) = n x^(n-1).

Why this answer is correct

f'(x) = 3x^2 - 12x + 11. At x = 2, f'(2) = 3(4) - 12(2) + 11 = 12 - 24 + 11 = -1.

Example

For f(x) = x^2 - 3x, f'(x) = 2x - 3, so at x = 1 the slope is -1.

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