Question

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?

Answer 1

is b the y-intercept?

Answer 2

of the tangent line?

Answer 3

oh i see

Answer 4

nvm i see the b lol

Answer 5

set y'=y''

Answer 6

Okay!

Answer 7

i dont know if that will help us lets see what heppens

Answer 8

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

Answer 9

so we have 4x^3+2(-6x^2)x+8=0
4x^3-12x^3+8=0
-8x^3+8=0
and so on...

Answer 10

you did see the typo above right when i wrote 4x^2 its suppose to be 4x^3

Answer 11

Yea lol! I'm going to see what I get!

Answer 12

so anyways we have 8x^3=8 so x^3=1 so x=1

Answer 13

if x=1 and b=-6x^2, then what does b=__

Answer 14

b=-6 and that's what the answer says!! :D

Answer 15

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

Answer 16

I understand! Yea it was a nice problem indeed!

Answer 17

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

Answer 18

not c but x lol

Answer 19

You were probably typing fast but yea I understand! Thanks!

Answer 20

ok have funs!