Derivative

1103164703

Level: 
A
The graph of \( f \) is given in the figure, where \( A \), \( B \) and \( C \) are points on the graph. If \( x_A \), \( x_B \) and \( x_C \) denote the \( x \)-coordinates of the points \( A \), \( B \) and \( C \) and if \( f' \) is the derivative of \( f \), then:
\( f'( x_A ) < f'( x_B ) < f'( x_C ) \)
\( f'( x_A ) < f'( x_B ) = f'( x_C ) \)
\( f'( x_A ) > f'( x_B ) = f'( x_C ) \)
\( f'( x_A ) > f'( x_B ) > f'( x_C ) \)
\( f'( x_A ) = f'( x_B ) < f'( x_C ) \)

1103164704

Level: 
A
The graph of \( f \) is given in the figure, where \( A \), \( B \) and \( C \) are points of the graph, and \( y \)-coordinate of the point \( B \) is the minimum value of the function \( f \). If \( x_A \), \( x_B \) and \( x_C \) denote the \( x \)-coordinates of the points \( A \), \( B \) and \( C \), and if \( f' \) is the derivative of \( f \), then:
\( f'( x_A ) < 0 \), \( f'( x_B ) = 0 \), \( f'( x_C ) > 0 \)
\( f'( x_A ) < 0 \), \( f'( x_B ) = 0 \), \( f'( x_C ) < 0 \)
\( f'( x_A ) > 0 \), \( f'( x_B ) < 0 \), \( f'( x_C ) < 0 \)
\( f'( x_A ) > 0 \), \( f'( x_B ) = 0 \), \( f'( x_C ) > 0 \)

1103164705

Level: 
A
The graph of \( f \) is given in the figure. Which of the following holds? (\( f' \) is the derivative of the function \( f \).)
\( f'(-1)=1 \), \( f'(2)=0 \), \( f'(4)=-2 \)
\( f'(-1)=1 \), \( f'(2)=2 \), \( f'(4)=0 \)
\( f'(-1)=0 \), \( f'(2)=0 \), \( f'(4)=-2 \)
\( f'(-1)=0 \), \( f'(2)=2 \), \( f'(4)=0 \)
\( f'(-1)=1 \), \( f'(2)=0 \), \( f'(4)=0 \)

1103164706

Level: 
A
The graph of \( f \) is given in the figure. Which of the following holds? (\( f' \) is the derivative of the function \( f \).)
\( f'(0)=1 \), \( f'(1) \) does not exist, \( f'(4)=-2 \)
\( f'(0)=1 \), \( f'(1)=0 \), \( f'(4)=-2 \)
\( f'(-1)=0 \), \( f'(2)=0 \), \( f'(3) \) does not exist
\( f'(-1)=1 \), \( f'(2)=0 \), \( f'(3)=0 \)

1103164707

Level: 
A
The graph of \( g \) is given in the figure. Which of the following holds? (\( g' \) is the derivative of the function \( g \).)
\( g'(-1)=0 \), \( g'(1)=2 \), \( g'(5)=-1 \)
\( g'(-1)=0 \), \( g'(1)=1 \), \( g'(5)=-1 \)
\( g'(-1)=0 \), \( g'(1)=2 \), \( g'(5)=2 \)
\( g'(-1)=-2 \), \( g'(1)=0 \), \( g'(5)=2 \)
\( g'(-1)=-2 \), \( g'(1)=2 \), \( g'(5)=2 \)

1103164708

Level: 
A
The graph of \( g \) is given in the figure. Which of the following holds? (\( g' \) is the derivative of the function \( g \).)
\( g'(1)=2 \), \( g'(2)=2 \), \( g'(4)=-1 \)
\( g'(-1)=0 \), \( g'(3) \) does not exist, \( g'(4)=3 \)
\( g'(-1) = -2 \), \( g'(3) \) does not exist, \( g'(4)=-1 \)
\( g'(1)=0 \), \( g'(2)=2 \), \( g'(4)=3 \)

1103164709

Level: 
A
The graph of \( f \) is given in the figure. Which of the following holds? (\( f' \) is the derivative of the function \( f \).)
\( f'(-1) \) does not exist, \( f'(1)=-\frac12 \), \( f'(4)=3 \)
\( f'(-2)=0 \), \( f'(1)=-2 \), \( f'(3) \) does not exist
\( f'(-2)=0 \), \( f'(2)=-\frac32 \), \( f'(4)=3 \)
\( f'(-1)=2 \), \( f'(1)=-\frac12 \), \( f'(3) \) does not exist

1103164710

Level: 
A
The graph of \( f \) is given in the figure. Which of the following holds? (\( f' \) is the derivative of the function \( f \).)
\( f'(-1)=0 \), \( f'(2)=-2 \), \( f'(4)=0 \)
\( f'(-1)=0 \), \( f'(2)=-\frac12 \), \( f'(4)=-3 \)
\( f'(-1)=0 \), \( f'(0)=0 \), \( f'(3)=0 \)
\( f'(0)=0 \), \( f'(2)=-1 \), \( f'(4)=0 \)
\( f'(0)=1 \), \( f'(2)=-2 \), \( f'(4)=-3 \)

2010002001

Level: 
A
Differentiate the following function. \[ f(x) = \pi -\frac{\ln 3}{x} \]
\(f'(x) = \frac{\ln 3 }{x^{2}} ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = 0 ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = \ln 3 ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = - \frac{\ln 3}{x^{2}} ;\ x\in \mathbb{R}\setminus \{0\}\)