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In a function f(x) = x^3 - 3x, what is the nature of the critical points?

Practice Questions

Q1
In a function f(x) = x^3 - 3x, what is the nature of the critical points?
  1. All critical points are local maxima.
  2. All critical points are local minima.
  3. There are both local maxima and minima.
  4. There are no critical points.

Questions & Step-by-Step Solutions

In a function f(x) = x^3 - 3x, what is the nature of the critical points?
  • Step 1: Find the first derivative of the function f(x) = x^3 - 3x.
  • Step 2: Set the first derivative equal to zero to find critical points.
  • Step 3: Solve the equation from Step 2 to find the values of x where the critical points occur.
  • Step 4: Use the second derivative test to determine the nature of each critical point (local maximum, local minimum, or saddle point).
  • Step 5: Analyze the results from Step 4 to conclude the nature of the critical points.
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