WEBVTT
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we want to know which of the following functions are
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solutions City differentially freaking. So this is our front
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differential equation. So we want to find our wide
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double primed and our wives and put those in Syria
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. So let's start with a Tony too far and
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wide over prime. So first, let's remember that
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the derivative Ah, cause, uh is negative,
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son. And the derivative of Sign is positive co
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sign X. So just some odd interviews. Do
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you remember? So let's take artery the sign we're
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gonna get Coast Onyx and I protected a room that
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we get negative sign. It's so we're just gonna
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put those into our equation here so we'll have negative
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sign picks plus sign X people to sign X and
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more left and saw. This is zero, and
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it's a sign X These are not equal. Therefore
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, we know A is not our answer for bee
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. We're under the same thing to define what crime
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, which is negative. Signed X and then we're
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gonna get our wide double product, which would be
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bring out our negative review and sign is co sign
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so negative co sign it. Put those into our
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equation, will have negative co signed X Please Costa
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on X, you bring down our right side.
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Far left side of zero will know Right side is
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the sine X and these are not the same.
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Therefore be Zlata. Answer Joyce Fighter Chrissy, we
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need to find what crimes in one double prime placement
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or equation. So it's Yvonne. Why prime?
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We're going to use product will. So how was
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the first times that a review of the second close
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? The circuit times the derivative with first we said
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before that will have one have that. Oh sonic
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close one have signed it. We're gonna do the
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same thing to find my double prime. We have
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to use product rule for this portion here. So
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we say the first times that ever got a second
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plus the second times that during the first it's just
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one upside and they were students. Bring down this
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portion here, but it's derivative and not derivative is
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one have co sign it. So we simplify.
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This will have negative one happy ex tonics plus 1/2
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co sign IX. That's one of those on exceptions
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one ex villages, but no one here or understood
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one. There So now we have We're why don't
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probably equation and r y equation and you just plug
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those into our function. We'll have negative 1/2 ex
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Sonics, close coast onyx lists or while equation and
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bring down our right hand side. So we simplify
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. We have a negative 1/2 X I next year
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on a positive here. So just counsel with each
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other and we have co sign X equals sine X
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over. This is not true. Therefore, seize
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letter answer toys either Does it look a Shame day
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? So even though we know that this has been
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an answer toys, we could still work it out
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. So we have our wives functions. I need
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to find our wives crime. So it's right there
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. You say the first times the ribbon of the
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second plus the spec It times that you're one of
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the first possible bodice will have positive 1/2 explore in
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it. Wilderness won her goes on it. Never
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use this upon our war double from equation. So
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take the first times that removed a second plus the
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second times that during your with the first and I
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was the derivative. This portion. Now it's like
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through this portion. So we have a minus one
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have sine X, but it changes. Sign because
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they removed could sign in the negative sign. But
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we simplify this. We'll have a one have ex
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co signed X and then just be one happens when
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half that's just one. So but signing? So
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now we have off the equation. So we need
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to plug into our differential equation here. Threw in
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a pregnancy. So you have want, huh?
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Thanks. Co sign it. Let's find it.
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Plus a negative one, huh? No. Co
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sign it and bring down our right hand side.
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Definitely. Look here and here. These subtract out
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they were left with signed X is able to sign
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it. Therefore, D is our answer choice.