# 159-8 Critical points

Hi all,

I was wondering how to get the critical points in the solution for 159-8 in “Finding Extreme Points” - been trying to solve it and probably missing something very simple but anyway, a little help/explanation would be much appreciated!

Hey, Mag.

The process is explained in the learn section:

You’ll need to first set 3x^2 - 2x to 0 and solve for x. Once you’ve found the critical point(s), you can analyze the slope around the point(s) to see if slope transitions from positive to negative or vice versa.

To analyze the direction of the slope, we use a sign chart. With a sign chart, we only care about if a given point in a region comes out positive or negative. This tool makes it great to analyze the direction of the slope (positive or negative).

Have you solved the equation 3x^2-3x=0? Have you checked the signs around the solutions (to create your sign chart)? What, specifically, are you having trouble with?

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Hey Bruno,

Best regards

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How exactly did you solve it? I am very poor at algebra and the farthest I got solving 3x**2 - 2*x = 0 was putting either constant on the either side. I even tried peeking at the answer and still did not get the values 0 and 2/3. I get stuck with the derivative at x ** 2 = (2/3) * x. Where did I go wrong?

Hey, Joachim.

If you want to ask Mag for help, that’s fine. But if you want to ask a question yourself, I suggest you ask it in a new post.

If your question is heavily related to this one, then please make sure you clarify how is it that my answer above isn’t helpful to you.

Will make a new post referencing this one.

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