A | math4u.vsb.cz

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.

2110002102

Level:

A

In one of the following pictures there is a graph of a function, which has null derivative at the point \(x = 3\). Choose this picture.

2110002101

Level:

A

In one of the following pictures there is a graph of a function, which has null derivative at the point \(x = 1\). Choose this picture.

2000003506

Level:

A

Calculate by how much do the arithmetic mean and the geometric mean of the roots of the equation \(x^2 -10x+16=0\) differ.

by \(1\)

by \(2\)

by \(3\)

do not differ

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