Question

Find points of inflection and discuss the concavity of the graph of the function.
F(x)=2x^3-3x^2-12x+5

Answer 1

I have so far
F ' (x) = \[F'(x) = 6x^2-6x-12\]
which gives you the critical #s of 2,-1
then
\[F''(x) = 12x-6\]
so possible inflection point is \[\frac{ 1 }{ 2 }\]

Answer 2

you've got the inflexcion point.
now, test for concavity

Answer 3

check the sign of the first derivative for any value of "x"

Answer 4

ok so I do not need to know the x intercept or the y intercept.

Answer 5

no wait..
there is no point of inflexion!!!!

Answer 6

\[
F''(2)=12(2)-6>0\\
F''(-1)=12(-1)-6<0
\]