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Okay, so we want the X values for which this function, which should look familiar, has a horizontal tangible. So in other words, we want to find X values such that F prime of X is equal to zero. So, in other words, this slope derivative is the slope of the tangent line. The slope of those tangent lines is your But remember that we already found at the prime of X In the previous example, F prime of X was equal to three X squared minus six x minus 24. Okay, we just did that by using the definition of the derivative. So if I want f Prime of X to be equal to zero, I'm really looking to solve three X squared, minus 66 minus 24 equals zero. So one thing we could do right off the bat, it's factor out of three, and that will help us try to see if we can factor. Yes, what is a quadratic function? So that's minus two. X factor out of three and then minus eight goes here. Okay. And I see that there's actually factors, so this is three times X minus four times x plus two. So, of course, one of these three things needs to be zero for the product to be zero using zero product property. And, of course, three can't be 03 is just three. So either excess for or X is negative. So these air the X values which our function has a horizontal dangerous.

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