Question

For what values of x do the curves y= (1+x^3)^2 and y= 2x^6 have the same slope??

The ans is 0 and 1, but I only get 1.. how do i get x=0?

Answer 1

y' = 2(1+x^3) (3x^2) y' = 12x^5
(6x)^2 (1+x^3) = 12x^5
x^3 = 1
x=1

Answer 2

6x^2(1+x^3)=12x^5
12x^5-6x^5-6x^2=0
6x^5-6x^2=0
6x^2(x^3-1)=0
6x^2=0 or x^3=1

Answer 3

how do you when will have 2 answers..cuz usually get 1 answer from dividing isnt it?