WEBVTT
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Okay, so we know that the derivative of a
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function f is three minus six over square root of
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X. And we're told that X not you two
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zero. All right, So, yeah, when
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is F prime equal to zero? And when is
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it undefined? Well, of course it's going to
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be undefined zero, but F is also under find
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it. Zero. So we will include that as
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a critical point, um, to see where the
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function is increasing or decreasing. So you can actually
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rewrite this if we put kind of a square root
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of X. Yeah. So you're all just isn't
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scratcher clicks a crime of eggs. I can write
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his three read X minus six. Overruled X And
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so I'm looking for a value backs that makes this
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equal to zero. Well, if I put in
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for I'm going to get square to force to three
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times two, six, six nine, six zero
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. So we have a critical point at for.
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And then, of course, we have this point
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where the derivative is undefined and also the functions undefined
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. Okay, so let's think about where the function
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is increasing or decreasing. Or, in other words
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, where death is going to be f crime is
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going to be positive or negative. Well, look
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at crime. Yeah, well, look a zero
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for Okay, Okay. So to the left of
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zero. Well, that's gonna be a problem,
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right? Because if crime is not defined for ex
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lessons here because if I try to plug in a
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number less than zero, I'm going to get,
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uh, the square root of a native number.
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So it's really undefined. Not here between zero and
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four. It's a If I plug in one,
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I get three minus six over one. That's gonna
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be a negative number. So f promise going to
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being negative between zero. And for what? If
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I plug in something greater than for this numerator is
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going to be positive over a positive number. So
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I'm going to get something positive. So then f
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is going to be decreasing between zero and four and
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then increasing between for infinity, Okay? And then
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if I look at my extreme well, zero,
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it's not going to be anything right, because the
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function just come on Xueling and redefined for ex greater
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than zero. So it seems like we just have
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a local men at X equals war because that's where
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the function changes from being decreasing to increasing