anonymous
  • anonymous
The function y=x^4 + bx^2 + 8x + 1 has a horizontal tangent and a point of inflection for the same value of x. What must be the value of b?
Mathematics
katieb
  • katieb
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myininaya
  • myininaya
is b the y-intercept?
myininaya
  • myininaya
of the tangent line?
myininaya
  • myininaya
oh i see

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myininaya
  • myininaya
nvm i see the b lol
myininaya
  • myininaya
set y'=y''
anonymous
  • anonymous
Okay!
myininaya
  • myininaya
i dont know if that will help us lets see what heppens
myininaya
  • myininaya
oh wait erase that we have 2 equations right the one with y' and the one with y'' set both = to zero so y'' gives us 12x^2+2b=0 which means b=-12x^2/2=-6x^2 so take y' which gives us 4x^2+2bx+8=0 and where you see that x plug in -6x^2
myininaya
  • myininaya
so we have 4x^3+2(-6x^2)x+8=0 4x^3-12x^3+8=0 -8x^3+8=0 and so on...
myininaya
  • myininaya
you did see the typo above right when i wrote 4x^2 its suppose to be 4x^3
anonymous
  • anonymous
Yea lol! I'm going to see what I get!
myininaya
  • myininaya
so anyways we have 8x^3=8 so x^3=1 so x=1
myininaya
  • myininaya
if x=1 and b=-6x^2, then what does b=__
anonymous
  • anonymous
b=-6 and that's what the answer says!! :D
myininaya
  • myininaya
did you understand the steps? do you want me to say why i did something or do you got it? this was a nice problem
anonymous
  • anonymous
I understand! Yea it was a nice problem indeed!
myininaya
  • myininaya
i seen another typo way up there it says replace c with -6x^2 thats suppose to be replace b with -6x^2 i cant type im sorry
myininaya
  • myininaya
not c but x lol
anonymous
  • anonymous
You were probably typing fast but yea I understand! Thanks!
myininaya
  • myininaya
ok have funs!

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