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 \(x_0=4\).
\( 0 < f'(x_0)< 1\)
\( -1 < f'(x_0)< 0\)
\( f'(x_0)>1\)
\( f'(x_0)< -1\)
Derivative
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 \(x_0=4\).
\(-1 < f'(x_0)< 0\)
\(0 < f'(x_0)< 1\)
\(f'(x_0)>1\)
\(f'(x_0)< - 1\)
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.
\( 4\)
\(3\)
\(5\)
\(6\)
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.
\(4\)
\(3\)
\(5\)
\(6\)
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?
\(3\)
\(2\)
\(1\)
\(4\)
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?
\(3\)
\(2\)
\(1\)
\(4\)
2010002106
Level:
A
How many of the following functions have the positive derivative at the point \(x = 3\)?
\(2\)
\(1\)
\(3\)
\(4\)
2010002105
Level:
A
How many of the following functions have the negative derivative at the point \(x = 1\)?
\(2\)
\(1\)
\(3\)
\(4\)
2110002104
Level:
A
In one of the following pictures there is a graph of a function, which is not differentiable at the point \(x = 3\). Choose this picture.
2110002103
Level:
A
In one of the following pictures there is a graph of a function, which is not differentiable at the point \(x = 1\). Choose this picture.
