To find the critical value of \( x \), we need to clarify the context, as the concept of critical value is used in different scenarios in mathematics. Here are some common contexts:

1. **Critical Points in Calculus:**
   To find critical points of a function \( f(x) \), you:
   - Take the derivative \( f'(x) \).
   - Set \( f'(x) = 0 \) and solve for \( x \).
   - Identify points where \( f'(x) \) does not exist as well.
   - The solutions are the critical values of \( x \), which may correspond to local maxima, minima, or inflection points.

2. **Critical Values in Hypothesis Testing:**
   In statistics, critical values correspond to cutoff points in hypothesis testing.
   - These values depend on the significance level \( \alpha \) (e.g., 0.05, 0.01) and the type of test (e.g., z-test, t-test).
   - You typically refer to statistical tables or use software to find critical values based on these inputs.

Could you provide more information on the function or scenario you're working with so I can assist you further?

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Here are 5 related questions:
1. Do you have a specific function for which you'd like to find the critical points?
2. Are you working with derivatives in calculus or hypothesis testing in statistics?
3. For calculus, would you like help differentiating a specific function?
4. In statistics, what significance level or distribution are you using to find critical values?
5. Are you solving an optimization problem requiring critical points?

**Tip:** In calculus, critical points are where the derivative is either zero or undefined. Always check the second derivative to classify the critical point.

Learn how to find the critical value of x in both calculus and hypothesis testing. This guide covers key concepts like derivatives, critical points, and statistical significance levels. Suitable for university-level students working with calculus and hypothesis testing.

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