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What is the critical point of the function f(x) = x^4 - 4x^3 + 6? (2023)

Practice Questions

Q1
What is the critical point of the function f(x) = x^4 - 4x^3 + 6? (2023)
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Questions & Step-by-Step Solutions

What is the critical point of the function f(x) = x^4 - 4x^3 + 6? (2023)
  • Step 1: Start with the function f(x) = x^4 - 4x^3 + 6.
  • Step 2: Find the first derivative of the function, which is f'(x) = 4x^3 - 12x^2.
  • Step 3: Set the first derivative equal to zero to find critical points: 4x^3 - 12x^2 = 0.
  • Step 4: Factor the equation: 4x^2(x - 3) = 0.
  • Step 5: Solve for x by setting each factor equal to zero: 4x^2 = 0 or x - 3 = 0.
  • Step 6: From 4x^2 = 0, we get x = 0. From x - 3 = 0, we get x = 3.
  • Step 7: The critical points are x = 0 and x = 3. We also consider x = 1 from the factorization.
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