mlddmlnog
Calculus. Help. :'(



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mlddmlnog
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for what nonnegative valuof b is the line given by \[y=\frac{ 1 }{ 3 }x+b\] perpendicular to the curve y=x^3?

UnkleRhaukus
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take the derivative (with respect to x) of both equations , what do you get?

mlddmlnog
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i got.. y'=1/3+b and y'=3x^2 ..

mlddmlnog
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waht do you do next?

UnkleRhaukus
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try the derivative of the first equation again ( you made a mistake)

mlddmlnog
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hm... i can't seem to find what my mistake was.. :/ is it the +b part??? because I do not know what to do with that...

UnkleRhaukus
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b is really bx^0

mlddmlnog
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so then, it would just be y'=1/3???

UnkleRhaukus
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thats better

UnkleRhaukus
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so you have found the first derivatives of the those lines,
the first derivative is the slope of the line

UnkleRhaukus
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the product of the slopes of perpendicular lines is 1

mlddmlnog
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yes.. uhm.. give me a few min to think please :)

UnkleRhaukus
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sure,

mlddmlnog
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ah, i'm struggling.. please help

UnkleRhaukus
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ok , so
\[m_1\times m_2=1\]
\[m_1=\frac13\qquad\qquad m_2=3x^2\]
solve for x

mlddmlnog
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x=+1 or 1 .

UnkleRhaukus
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good

UnkleRhaukus
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now set \[y_1=y_2\]
take the first case (x=1) and find b

UnkleRhaukus
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does that make sense?

mlddmlnog
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yes it does :) sorry. open study was being so slow .but i get it now. thank you! :)

UnkleRhaukus
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what did you you get for an answer/

mlddmlnog
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no what do i do..?