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# Analyzing mistakes when finding extrema (example 1)

Analyzing the work of someone who tried to find extrema of a function, to see whether they made mistakes.

## Want to join the conversation?

• Isn't this a trick question? Does x^3-6*x^2+12x actually have any relative extrema?
• No, it doesn't. It's derivative is 3x²-12x+12, which factors as 3(x-2)², which is 0 at 2 and positive elsewhere. Since extrema require the derivative to switch between positive and negative, this function has no extrema.
• so any point where the derivative is 0 is called a critical point right??
(1 vote)
• For a continuous function, anywhere in the domain of the function where the derivative is either 0 or undefined is called a critical point.
• This isn't really related to the topic, but if we had an equation like
12x^2 + 4x - 4
Can we factor out a 4x from the terms even though only two of them have it?