WEBVTT
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All right. See you. Becks equals X to
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the two thirds times X plus five. Okay,
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so the derivative, it's gonna be two thirds next
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to the minus two third. Who next? Tonight
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, it's one third times X plus five plus X
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to the two thirds. And I'm gonna multiply the
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top bottom by X to the one third, actually
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, three times x to the wondered. So get
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two times X plus five plus just, uh,
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three x all over three X to the one third
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. So to find a critical points, where does
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cheap Prime equals? Zero. We want to solve
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two x plus ten plus three x zero R five
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x this planet zero or nexus Negative too. And
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then where's Ji Prime? Undefined. Well, that's
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easy. That's just all next zero. Okay,
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so find the intervals there. Jeez, Increasing or
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decreasing so well put. Negative. Two zero.
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I've been virtually crime When city. So here's our
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numerator When x is less the negative to the numerator
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is negative And the denominators negatives of executive and then
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we go between native two and zero the the numerator
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becomes positive, but the denominator is still negative.
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Zits. Come on listen. Sorry when X is
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less than a year to their both. Negative.
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So that's a positive betweennegative two and zero. The
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numerator is positive in the denominator is negative and then
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the next is greater than zero. They're both positive
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. So, g, it's going to be increasing
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from minus infinity to minus two, decreasing from negative
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to zero and then increasing from zero to infinity.
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Good. And so, Lou onesie, We have
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a local max Where at see negative two. Right
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, Because the function is changing from increasing decreasing,
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and the value is going to be three Cambridge for
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all right. Three pussy, three cube root of
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yeah, you two for good. And then we
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have a local men at zero here, and there's
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gonna be no absolute max syrups that men, because
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the function is increasing from mega infinity and then increasing
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to infinity