Concavity and Points of Inflection

Concave up in   $$\left(-\infty,-1\right)$$   

Concave down in    $$\left(-\infty,-1\right)$$  

Concave down in  $$\left(-1,\infty\right)$$  

Concave down in     $$\left(-2,0\right)$$  

Concave up in    $$\left(-1,\infty\right)$$  

Concave down in  $$\left(-\infty,1\right)$$  , Concave up in $$\left(5,\infty\right)$$  and the point of inflection at x=1.

Concave down in  $\left(-\infty,1\right)$ and $$\left(2,\infty\right)$$ , with no point of inflection.

Concave up in  $\left(-\infty,1\right)$ and $$\left(2,\infty\right)$$ , with no point of inflection.

Concave up in $$\left(-\infty,\infty\right)$$  with no point of inflection.

No point of inflection

Points 3 and 5

Points 1, 3, 5 and 7

Points 1, 2, 3, 4, 5, 6 and 7

Points 2, 4 and 6

Where x = 8

Where x = 4

Where x = 0

No inflection point

Where x = -8