Function Behavior

2110012504

Level: 
B
Choose the graph of a function $f$ that satisfies \begin{gather*} f'(1) \text{ does not exist}, \\ f''(x) < 0 \text{ if } x < 1 , \\ f''(x) < 0 \text{ if } x > 2, \\ f''(x) > 0 \text{ if } 1 < x < 2 \end{gather*} ($f'$ is the derivative of a function $f$, $f''$ is the second derivative of a function $f$).

9000142001

Level: 
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-1,0)\) and \((1,\infty )\), concave down on \((-\infty ,-1)\) and \((0,1)\), inflection at \(x = 0\)
concave up on \((-\infty ,-1)\) and \((0,1)\), concave down on \((-1,0)\) and \((1,\infty )\), inflection at \(x = 0\)
concave up on \((-1,0)\) and \((1,\infty )\), concave down on \((-\infty ,-1)\) and \((0,1)\), no inflection
concave up on \((-1,0)\cup (1,\infty )\), concave down on \((-\infty ,-1)\cup (0,1)\), inflection at \(x = 0\)

9000142002

Level: 
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ,1)\), concave down on \((1,\infty )\), inflection at \(x = 1\)
concave up on \((1,\infty )\), concave down on \((-\infty ,1)\), inflection at \(x = 1\)
concave up on \((-\infty ,0)\), concave down on \((0,\infty )\), inflection at \(x = 0\)
concave up on \((-\infty ,1)\), concave down on \((1,\infty )\), inflection at \(x = \frac{2} {3}\)

9000142003

Level: 
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ,0)\) and \((1,\infty )\), concave down on \((0,1)\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)
concave up on \((-\infty ,0)\cup (1,\infty )\), concave down on \((0,1)\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)
concave up on \((0,1)\), concave down on \((-\infty ,0)\) and \((1,\infty )\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)
concave up on \((-\infty ,0)\) and \((1,\infty )\), concave down on \((0,1)\), a unique inflection at \(x = 0\)