Applications of derivatives

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 \(x = 1\).

9000145405

Level: 
C
Identify a true statement on the function \(f(x) = \frac{1} {4}x^{4} -\frac{2} {3}x^{3} -\frac{3} {2}x^{2} + 2\text{ on }\left (-2;4\right )\).
The function \(f\) has a local maximum at the point \(x = 0\).
The function \(f\) has a local minimum at the point \(x = 0\).
The global maximum of \(f\) on this interval is at \(x = 0\).
The global minimum of \(f\) on this interval is at \(x = 0\).

9000145406

Level: 
C
Identify a true statement on the function \(f(x) = x^{3} - 12x + 20\text{ on }\left (-3;4\right )\).
The global minimum of \(f\) on this interval is at \(x = 2\).
The global maximum of \(f\) on this interval is at \(x = 2\).
The function \(f\) has a local minimum at the point \(x = -2\).
The global minimum of \(f\) on this interval is at the point \(x = -2\).

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.