WEBVTT
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Kate. So four problem five were given that the
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roof too. That iss X minus one Experts too
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. And times X minus three. All right,
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so what we need to do is first find Theo
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Critical points. That is, when next, a
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sequel to one and access equal to negative too.
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And access equal to three. And any of these
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will make our directive to be equal to zero.
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So these are the art of critical points. Now
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, for our king, you need to find the
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increase interval and open on dhe decrease interval. So
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what we need to do first less lead is derivative
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to be positive, Kate. So four problem five
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were given that the roof too. That is X
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minus one. Experts too. And times X minus
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three. All right, So what we need to
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do is first find Thea. Now, the only
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thing we need to do is to solve this sub
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Vizzini equality. Now they are 22 conditions. We
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need to consider here the first condition ISS. All
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these three terms are all positive. So that is
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to say, our expert minus one is positive and
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article points. That is when next a sequel to
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one and access equal to negative too, and access
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equal to three. And any of these will make
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our directive to be equal to zero. So these
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are the art of critical points. Now are you
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need to find the increase interval and open on dhe
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decrease interval. So what we need to do first
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less. Let is derivative to be positive or X
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plus two is positive and X minus three. It's
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positive and combine these two these three inequalities then we
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have. So what we have will be X B
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bigger than three, and the second condition we need
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to consider is to have two negative things that is
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now. The only thing we need to do is
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to solve this sub Vizzini equality. Now they are
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22 conditions that we need to consider here the first
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condition ISS. All these three terms are all positive
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. So that is to say, our expert minus
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one is positive and our either x one x minus
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. Well experts, too, are negative or X
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plus two plus express to an X minus. Three
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are negative or X minus one and x minus.
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Three are negative. So that is we have X
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minus one. Uh, I'll start a new page
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, so our condition, too, will be X
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plus two is positive and X minus three. It's
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faster and combine these two these three inequalities then we
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have. So what we have will be X B
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bigger than three, and the second condition we need
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to consider is too have to negative things. That
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is two negative terms. Okay, so we to
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neck to turn to connect the terms. Let's first
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consider X minus one is next to and X plus
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two. It's not, too, and X minus
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three is positive. We cannot let the third time
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either x one x minus. While experts, too
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, are negative or experts too, plus express to
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an X minus, three are negative or X minus
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one and X minus. Three are negative. So
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that is we have X minus one. Uh,
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I'll start a new page so our condition, too
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, will be to connective. Otherwise, solver are
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a whole equation will be connected. So this is
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the first condition. Or we could have the 2nd
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2nd of sorry for this is the first inequality.
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Or we could have the second inequality which is make
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explains one neck, too. And X plus two
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house, too and X minus three. Two negative
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terms. Okay, so we too negative term to
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connect the terms nest first, consider X minus one
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is next to and X plus two. It's not
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, too, and X minus three is past it
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. We cannot let the third term to pit or
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the last the last in qualities we need to think
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about. ISS X minus one wants to and X
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plus two negative and X minus tree naked. So
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by solving these three set, it's three sets of
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inequalities. What we have in the end is connective
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. Otherwise, solver are a whole equation will be
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connected. So this is the first condition. Or
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we could have the 2nd 2nd of the purchases.
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The first the inequality. Or we can have the
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second inequality, which is make explains one next to
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and X plus two house too and X minus three
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night, um, empty for the first set of
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inequalities and negative too smaller than acts smaller than one
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. It's our second date. Quality is a solution
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of our over a seven second set of inequalities and
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the third in qualities or so gives us. Um
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Empty said so Combine one and two or the last
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. The last in qualities we need to think about
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it is X minus. One wants to and X
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plus two negative and X minus tree Noted So by
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solving these three set is three sets of inequalities.
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What we have in the end is due. We
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conclude that on interval from negative too from one union
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, three from infinity dysfunction will increase and from negative
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that could be penetrated to connect it to you again
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. 123 dysfunction will decrease. Okay, now,
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R. C, we want to find a local
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, make Mexico the local minimum. So Daddy's just
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till, um, empty for the first set of
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inequalities and negative too smaller than acts smaller than one
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. It's our second date. Quality is a solution
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of our of our set a second set of inequalities
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and the third in qualities or so gives us,
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um empty said so Combine one and to some of
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these, uh, these two in a boat here
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. So first we reach our from from negative 2
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to 1. We reach our local Mexico because the
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function is increasing. And after one it will decrease
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from 1 to 3. So that one will be
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loco will be a local Mexico and our local minimum
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The officer from Active Benedetti connected to the function This
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always increase, always decreasing you. We conclude that
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on interval from negative too from one union three wrong
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infinity dysfunction will increase and from negative that could be
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penetrated to connect it to you again. 123 dysfunction
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will decrease. Okay now R c. We want
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to find a local make Mexico the local minimum.
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So Daddy's just the opposite and from neck to 2
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to 1 to function were increased, So elected to
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will be local minimum and also from 1 to 3
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the function decrease and from three to infinity dysfunction will
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increase. So f three we also be a local
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minimal so