For the following graph, find the open intervals for which the function is concave up or concave down. Identify any inflection points.

• A. Concave up: $\left(-\infty,0\right)$, $\left(1,\infty\right)$; Concave down: $\left(0,1\right)$; Inflection points: $\left(0,0\right)$, $\left(1,1\right)$
• B. Concave up: $\left(-\infty,0\right)$; Concave down: $\left(0,\infty\right)$; Inflection points: $\left(0,0\right)$
• C. Concave down: $\left(-1,0\right)$, $\left(1,\infty\right)$; Concave up: $\left(0,1\right)$; Inflection points: $\left(0,0\right)$, $\left(1,1\right)$
• D. Concave up: $\left(-1,0\right)$, $\left(1,\infty\right)$; Concave down: $\left(0,1\right)$; Inflection points: $\left(-1,1\right)$, $\left(0,0\right)$, $\left(1,1\right)$

Answer: (A)