What is the difference between a critical point and a stationary point?

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What is the difference between a critical point and a stationary point?

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Answer 1 · 2015-03-29T03:48:51

$(x_0,f(x_0))$ is a stationary point of $f(x)$ if $f(x_0)$ and $f'(x)$ exist and is equal to $f'(x_0)=0$

$(x_0,f(x_0))$ is a critical point of $f(x)$ if $f(x_0)$ exists and either
$f'(x_0)$ does not exist (that is $f(x)$ is not differentiable at $x_0$
or
$f'(x_0) = 0$

For example $f(x) = sqrt(1-1/(x^2+1))$ is not differentiable at $(0,0)$ , so $(0,0)$ is a critical point of $f(x)$ but not a stationary point.
graph{sqrt(1-1/(x^2+1)) [-2.434, 2.434, -1.215, 1.218]}

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What is the difference between a critical point and a stationary point?

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