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