Applications of derivatives

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 \(x = 0\)

9000142004

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

9000142005

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 \(x_{1} = -1\), \(x_{2} = 0\) and \(x_{3} = 1\)
concave up on \((-1;0)\cup (1;\infty )\), concave down on \((-\infty ;-1)\cup (0;1)\), inflection at \(x_{1} = -1\), \(x_{2} = 0\) and \(x_{3} = 1\)
concave up on \((-\infty ;-1)\) and \((0;1)\), concave down on \((-1;0)\) and \((1;\infty )\), inflection at \(x_{1} = -1\), \(x_{2} = 0\) and \(x_{3} = 1\)
concave up on \((-\infty ;-1)\cup (0;1)\), concave down on \((-1;0)\cup (1;\infty )\), inflection at \(x_{1} = -1\), \(x_{2} = 0\) and \(x_{3} = 1\)

9000142006

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 \((0;1)\), a unique inflection at \(x = 0\)
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 \((0;1)\), a unique inflection at \(x = 0\)
concave up on \((0;1)\), concave down on \((-\infty ;0)\) and \((1;\infty )\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)

9000145401

Level: 
B
Identify a true statement on the function \(f(x) = 2x^{3} + 3x^{2} - 12x - 12\).
The function \(f\) has a local maximum at the point \(x = -2\).
The function \(f\) has a local minimum at the point \(x = -2\)..
The global maximum of \(f\) on \(\mathbb{R}\) is at \(x = -2\).
The global minimum of \(f\) on \(\mathbb{R}\) is at \(x = -2\).

9000145402

Level: 
B
Identify a true statement about the function \(f(x) = 2x^{2} -\frac{x^{4}} {4} \).
The global maximum of \(f\) on \(\mathbb{R}\) is at \(x = 2\) and \(x = -2\).
The global minimum of \(f\) on \(\mathbb{R}\) is at \(x = 2\) and \(x = -2\).
The function \(f\) has a local minimum at the point \(x = 2\).
The function \(f\) has a local minimum at the point \(x = -2\).

9000145403

Level: 
B
Identify a true statement on the function \(f(x)= \frac{4-3x} {x\left (1-x\right )}\).
The function \(f\) has a local minimum at the point \(x = \frac{2} {3}\).
The function \(f\) has a local maximum at the point \(x = \frac{2} {3}\).
The global maximum of \(f\) on \(\mathbb{R}\setminus \{0.1\}\) is at \(x = \frac{2} {3}\).
The global minimum of \(f\) on \(\mathbb{R}\setminus \{0.1\}\) is at \(x = \frac{2} {3}\).