#how do I find the answer to b, I found dx/dy

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high fossil
rose boltBOT
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reef cedar
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@high fossil do you know the equation to a straight line?

high fossil
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y=mx+c

reef cedar
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line of slope m passing through (p, q)

high fossil
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x=k

reef cedar
high fossil
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Oh

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Not what you asked for

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My bad

reef cedar
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but yeah you did get a part of the problem's idea right

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the slope will be infinite

high fossil
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Yep

reef cedar
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so the denominator of f' has to go to?

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0

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and when does that happen?

high fossil
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?

reef cedar
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okay wait let me get a graph thingy

high fossil
reef cedar
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but here ngl you can just find P, Q by seeing when "x=k" has exactly one solution

high fossil
reef cedar
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2y^2+6=k(3y-3)
2y^2-3ky+6+3k=0
the discriminant is (-3k)^2-4(3k)(2) which has to be 0 here

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it touches the graph at exactly one y coordinate

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does this work

high fossil
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Uhm but the answers are x=-4/3 and x=4

reef cedar
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gilbert F

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okay use the derivatives

reef cedar
high fossil
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Okay idgi

The answer says you have to equate the denominator of the derivative I got from part a to 0

So 2y^2 -4y - 6 = 0

reef cedar
high fossil
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I understand it’s because the slope is infinity but I also don’t understand the full logic could you please explain that part?

reef cedar
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this yields the right answer

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i checked

reef cedar
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like this

high fossil