WEBVTT
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Okay, so you have dysfunction. That's a hex
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. Because execute, tell us three X squared twenty
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four. Thanks. Plus two. All right.
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Ever asked to find a local extreme the values of
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those relative extreme. So the first thing we want
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to do is take the derivative to find the critical
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points knows their ex values where the function is either
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at the derivative of the function is either zero r
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undefined. Those x coordinates are in the domain of
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functioning as well. So here's the derivative, and
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this is never going to be under find it just
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a polynomial. But if we said equal to zero
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, get a quadratic equation, we could use the
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quadratic formula, or we could just be hopeful that
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it factors. And the first thing we notice is
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that all these coefficients are divisible by three close to
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about three. So get X squared plus two x
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st. And if I try to factor this,
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get it serious? Uh, cause Yeah, good
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. Here. Zero Nicole's. Hey, Well,
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see, I need two numbers that multiple. I
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d give me negative eight and had to give me
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two. So should be negative for into you spoil
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this hour. You should get same thing that you
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do, sir. Critical points are negative for and
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too right. So now we can draw our number
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. Land implied thank you for and Teo. And
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we want to test values of the derivatives to see
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whether they're positive or negative to see whether the function
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is increasing or decreasing around these critical points. Uh
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,*** Negative five to the left of negative for
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when you pick something Betweennegative twos because zero. Then
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we can pick three. And I wanna plug these
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red values into the derivatives. If I plug it
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into five in seeing it's seventy five minus thirty miles
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. Twenty four, that's going to be positive.
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And I really only care about the sign on the
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door of grease that has a functioning saying at zero
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again negative talk for easy to see. It's of
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its negative zero and then three twenty seven points seventeen
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. I strongly for that's very positive. Can unplugging
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these into the derivative, right? So now we
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see the general shape of our Graff. We are
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increasing up to negative for than decreasing, then increasing
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after two. So that's kind of our graph Looks
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like, So we have a relative. Maxima had
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begged for relative minima, too, and we can
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find the values of those local maximum Emma so negative
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four. So the plug negative for back into the
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function to get the value of the local Maxima here
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. So we have, uh, it's negative down
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. So the first term negative for cute that's negative
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. Sixty four and then plus correct three times sixteen
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or hate and then minus to the twenty four times
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negative for hiss. Positive ninety six plus thanks and
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then us two. Good answer. That's going to
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be all right. So*** before plus forty eight
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, that's going to give me a value of negative
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sixteen plys ninety six since takeaway sixteen ninety six eighty
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and then and to being a game, too.
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And then the value of the function hat to value
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of the minimum to local minima. This can't be
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ate too cute, plus three times for twelve minus
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twenty four times. Two. Paint us, too
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. It's twenty miles forty eight nine twenty eight plus
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two. Thank you tive twenty six p that value