Problem

The critical number of $f(x)=x^{2}-2 x+9$ is

Answer:

Answer

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Answer

The critical number of the function \(f(x)=x^{2}-2 x+9\) is \(\boxed{1}\).

Steps

Step 1 :The critical numbers of a function are the x-values where the derivative of the function is either zero or undefined. So, to find the critical numbers of the function \(f(x)=x^{2}-2 x+9\), we first need to find its derivative.

Step 2 :The derivative of the function \(f(x)=x^{2}-2 x+9\) is \(f'(x)=2x-2\).

Step 3 :Now, we need to find the x-values where this derivative is zero.

Step 4 :The critical number of the function \(f(x)=x^{2}-2 x+9\) is \(\boxed{1}\).

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