2010002105
Level:
A
How many of the following functions have the negative derivative at the point \(x = 1\)?
\(2\)
\(1\)
\(3\)
\(4\)
Derivative
2010002106
Level:
A
How many of the following functions have the positive derivative at the point \(x = 3\)?
\(2\)
\(1\)
\(3\)
\(4\)
2010002107
Level:
A
Given the function \(f(x)=-5(x-1)^3+3(x-1)^5-2\) (see the picture), at how many points has this function null derivative?
\(3\)
\(2\)
\(1\)
\(4\)
2010002108
Level:
A
Given the function \(5(x+2)^3-3(x+2)^5+2\) (see the picture), at how many points has this function null derivative?
\(3\)
\(2\)
\(1\)
\(4\)
2010002109
Level:
A
There is a part of the function
\[
f(x)=\left\{\begin{matrix}
&-|x+2|+4,& x \in (-\infty;1)\setminus\{-3\} \\
&1, & x \in [ 1;2) \\
&2, & x \in [ 2;5] \\
&3-(x-6)^{-2} & x \in (5;\infty)\setminus \{6\}\\
\end{matrix}\right.
\]
in the picture. Use the graph to determine at how many points of the given interval \([ -4;8 ]\) is the function \(f\) defined and is not differentiable.
\(4\)
\(3\)
\(5\)
\(6\)
2010002110
Level:
A
There is a part of the function
\[
f(x)=\left\{\begin{matrix}
&(x+6)^{-2}+2& x \in (-\infty;-5)\setminus\{-6\} \\
&3, & x \in [ -5;-3 ] \\
&1, & x \in (-3;-1) \\
&|x-1|-1& x \in [ -1,\infty)\setminus \{6\}\\
\end{matrix}\right.
\]
in the picture. Use the graph to determine at how many points of the given interval \([ -8; 7 ]\) is the function \(f\) defined and is not differentiable.
\( 4\)
\(3\)
\(5\)
\(6\)
2010002111
Level:
A
There is a part of the function \(f\) and the point \(x_0\) in the picture. Choose the true statement about the derivative at the point \(x_0=4\).
\(-1 < f'(x_0)< 0\)
\(0 < f'(x_0)< 1\)
\(f'(x_0)>1\)
\(f'(x_0)< - 1\)
2010002112
Level:
A
There is a part of the function \(f\) and the point \(x_0\) in the picture. Choose the true statement about the derivative at the point \(x_0=4\).
\( 0 < f'(x_0)< 1\)
\( -1 < f'(x_0)< 0\)
\( f'(x_0)>1\)
\( f'(x_0)< -1\)
2010005201
Level:
A
Given the function \( f\colon y=2x^4-x^2+4x \), find \( f'(-1) \).
\( -2\)
\( 14 \)
\( -6 \)
\( -10 \)
\( 2 \)
2010005202
Level:
A
Given the function \( f\colon y=\frac12 x^2-4\), determine all the values of \( x \) (\( x\in\mathbb{R} \)) for which \(|f' (x)|=1 \).
\( x_1=1 \), \( x_2 =-1 \)
\( x=1\)
\( x_1=2 \), \( x_2 =-2 \)
\( x=2\)
\( x=-1 \)