Applications of derivatives

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 \(x = \frac{2} {3}\).