Why isn’t this considered a critical point?

[The Velociraptors]

Why aren’t x=2 and x=-2 critical values? I thought critical values are where the slope=0 or is undefined. So according to the answer key, why aren’t the points circled in green critical points, and why is x=3 a critical point (according to the answer key)? When are x-intercepts critical points? Any additional reading would also help. Thank you.

 

[skeeter]

critical values of a function, f(x), are those values of x where f’(x) = 0 or is undefined

NOTE that the graphs are derivatives of f, not f(x).

 

[Dr.Peterson]

View attachment 34623Why aren’t x=2 and x=-2 critical values? I thought critical values are where the slope=0 or is undefined. So according to the answer key, why aren’t the points circled in green critical points, and why is x=3 a critical point (according to the answer key)? When are x-intercepts critical points? Any additional reading would also help. Thank you.

In case you don't see it, note the yellow highlights:

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I've seen problems like this before; you have to read very carefully and make no assumptions based on appearances!

They want critical values for f, not for the graph you see; so you want to find where the graph, f'(x), is zero.

In part b, they don't label the vertical axis, so it's even more subtle.

 

[Steven G]

You are correct when you think that x=2 and x=-2 critical values. The only problem is that they are critical points of f'(x) and you are being asked for the critical points of f(x).

 

[Dr.Peterson]

You are correct when you think that x=2 and x=-2 [are] critical values. The only problem is that they are critical points of f'(x) and you are being asked for the critical points of f(x).

Actually, not quite! As I read the graph, those are both a little off (and even the intercept at -4 is not exact:

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But of course that doesn't really matter (apart from the inaccuracy at -4, which we are probably supposed to ignore anyway).

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[Steven G]

Actually, not quite! As I read the graph, those are both a little off (and even the intercept at -4 is not exact:

I just didn't want to confuse the OP more than necessary.