C

9000146209

Level: 
C
Factor the following expression. \[ 27a^{3} - 8b^{9} \]
\(\left (3a - 2b^{3}\right )\left (9a^{2} + 6ab^{3} + 4b^{6}\right )\)
\(\left (3a + 2b^{3}\right )\left (9a^{2} - 6ab^{3} + 4b^{6}\right )\)
\(\left (3a - 2b^{3}\right )\left (9a^{2} + 12ab^{3} + 4b^{6}\right )\)
\(\left (3a + 2b^{3}\right )\left (9a^{2} - 12ab^{3} + 4b^{6}\right )\)

9000146210

Level: 
C
Factor the following expression. \[ 64x^{6} + 125 \]
\(\left (4x^{2} + 5\right )\left (16x^{4} - 20x^{2} + 25\right )\)
\(\left (4x^{2} - 5\right )\left (16x^{4} + 20x^{2} + 25\right )\)
\(\left (4x^{2} + 5\right )\left (16x^{3} - 20x^{2} + 25\right )\)
\(\left (4x^{2} - 5\right )\left (16x^{3} + 20x^{2} + 25\right )\)

9000145401

Level: 
C
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: 
C
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: 
C
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 \(x = \frac{2} {3}\).

9000145404

Level: 
C
Identify a true statement about the function \(f(x) = x^{3} - 3x^{2} + 3x + 2\).
There is neither local minimum nor maximum of \(f\).
The function \(f\) has a local maximum at the point \(x = 1\).
The function \(f\) has a local minimum at the point \(x = 1\).
The global minimum of \(f\) on \(\mathbb{R}\) is at \(x = 1\).

9000145407

Level: 
C
Identify a true statement on the function \(f(x) = x^{4} - 8x^{3} + 22x^{2} - 24x + 12\).
The global minimum of \(f\) on \(\mathbb{R}\) is at \(x = 1\) and \(x = 3\).
The global maximum of \(f\) on \(\mathbb{R}\) is at \(x = 2\).
The local minima of \(f\) are at \(x = 1\) and \(x = 2\).
The local maximum of \(f\) is at \(x = 3\).

9000145408

Level: 
C
Identify a true statement on the function \(f(x) = \left (x - 1\right )^{3}\left (x + 1\right )^{2}\).
The function \(f\) has neither local minimum nor maximum at \(x = 1\).
The global maximum of \(f\) on \(\mathbb{R}\) is at \(x = -1\).
The function \(f\) has a local maximum at \(x = -\frac{1} {5}\).
The function \(f\) has three local extrema. These extrema are at \(x = 1\), \(x = -1\) and \(x = -\frac{1} {5}\).

9000145409

Level: 
C
Identify a true statement on the function \(f(x) = 1 + 2x^{2} -\frac{1} {4}x^{4}\).
The global maximum of \(f\) on \(\mathbb{R}\) is at \(x = 2\) a \(x = -2\).
The function \(f\) has a global minimum on \(\mathbb{R}\).
The function \(f\) has a local maximum at \(x = 0\).
The function \(f\) has neither local minimum nor maximum.