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If f(x) = x^3 - 3x^2 + 4, find the critical points of f.

Practice Questions

Q1
If f(x) = x^3 - 3x^2 + 4, find the critical points of f.
  1. x = 0, 1, 2
  2. x = 1, 2
  3. x = 0, 2
  4. x = 1

Questions & Step-by-Step Solutions

If f(x) = x^3 - 3x^2 + 4, find the critical points of f.
  • Step 1: Start with the function f(x) = x^3 - 3x^2 + 4.
  • Step 2: Find the derivative of the function, which is f'(x). The derivative tells us the slope of the function.
  • Step 3: Calculate the derivative: f'(x) = 3x^2 - 6x.
  • Step 4: Set the derivative equal to zero to find critical points: 3x^2 - 6x = 0.
  • Step 5: Factor the equation: 3x(x - 2) = 0.
  • Step 6: Solve for x by setting each factor equal to zero: 3x = 0 gives x = 0, and x - 2 = 0 gives x = 2.
  • Step 7: The critical points are x = 0 and x = 2.
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