Find the concavity.

Question

For f(x)=6x⁴-x²

I got downwards correct as (-1/6,1/6)

I got upwards incorrect:

(-infinity,-1/6) and also wrong (1/6, infinity)

Answer 1

looks ok to me

y = 6x^4 - x^2

y' = 24x^3 - 2x

y'' = 72x^2 - 2

0 = 72x^2 - 2

2/72 = x^2

1/36 = x^2

x = +or- 1/6

interval sample test x f''(x)

x< -1/6 -1 70 <-- concave up

-1/6 < x < 1/6 0 -2 <-- convace down

x>1/6 1 70 <-- concave up

Try (-infinity, 1/6) U (1/6, infinity)