anonymous
  • anonymous
Calculus. Help. :'(
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
for what non-negative valuof b is the line given by \[y=-\frac{ 1 }{ 3 }x+b\] perpendicular to the curve y=x^3?
UnkleRhaukus
  • UnkleRhaukus
take the derivative (with respect to x) of both equations , what do you get?
anonymous
  • anonymous
i got.. y'=-1/3+b and y'=3x^2 ..

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anonymous
  • anonymous
waht do you do next?
UnkleRhaukus
  • UnkleRhaukus
try the derivative of the first equation again ( you made a mistake)
anonymous
  • anonymous
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
  • UnkleRhaukus
b is really bx^0
anonymous
  • anonymous
so then, it would just be y'=-1/3???
UnkleRhaukus
  • UnkleRhaukus
thats better
UnkleRhaukus
  • UnkleRhaukus
so you have found the first derivatives of the those lines, the first derivative is the slope of the line
UnkleRhaukus
  • UnkleRhaukus
the product of the slopes of perpendicular lines is -1
anonymous
  • anonymous
yes.. uhm.. give me a few min to think please :)
UnkleRhaukus
  • UnkleRhaukus
sure,
anonymous
  • anonymous
ah, i'm struggling.. please help
UnkleRhaukus
  • UnkleRhaukus
ok , so \[m_1\times m_2=-1\] \[m_1=-\frac13\qquad\qquad m_2=3x^2\] solve for x
anonymous
  • anonymous
x=+1 or -1 .
UnkleRhaukus
  • UnkleRhaukus
good
UnkleRhaukus
  • UnkleRhaukus
now set \[y_1=y_2\] take the first case (x=-1) and find b
UnkleRhaukus
  • UnkleRhaukus
does that make sense?
anonymous
  • anonymous
yes it does :) sorry. open study was being so slow .but i get it now. thank you! :)
UnkleRhaukus
  • UnkleRhaukus
what did you you get for an answer/
anonymous
  • anonymous
no what do i do..?

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