Question

Find the interval on which the curve is concave upward.

Answer 1

first derivative is \[\frac{1}{6+x+3x^2}\] find the second derivative, see where it is positive

Answer 2

\[F''(x)=\frac{-(1+6x)}{(6+x+3x^2)^2}\]
the denominator is always positive, solve \[-1-6x>0\] for \(x\)

Answer 3

-6x > 1
x < -1/6

Answer 4

yeah looks good

Answer 5

what would that interval be? (-infinity, -1/6] ?