2110013901
Level:
A
The pictures show parts of graphs of functions that are increasing on the interval \([1;5]\). Choose the picture showing the part of the graph of the function \(f(x)=\frac{5x-1}{x+1}\).
Applications of derivatives
2110013902
Level:
A
The pictures show parts of graphs of functions that are decreasing on the interval \([1;5]\). Choose the picture showing the part of the graph of the function \(f(x)=\frac{x+7}{x+1}\).
2110020003
Level:
A
A function \(f\) is given by the formula \(f(x)=(x+3)^3-3x-6\). Choose the picture that shows a part of the graph of this function.
2110020004
Level:
A
A function \(f\) is given by the formula \(f(x)=-(x-3)^3+3x-12\). Choose the picture that shows a part of the graph of this function.
9000062409
Level:
A
Find the first derivative of the function
\(f(x) = x^{2} + x - 6\) at each of the
\(x\)-intercepts.
\(- 5;\ 5\)
\(- 3;\ 7\)
\(- 7;\ 6\)
\(- 9;\ 6\)
9000070401
Level:
A
Given the function \(f(x) = x^{2} + x - 2\), find
the intervals where \(f\)
is an increasing function.
\(\left (-\frac{1}
{2};\infty \right )\)
\(\left (-3;\infty \right )\)
\(\left (-2;\infty \right )\)
\(\left (-1;\infty \right )\)
9000070402
Level:
A
Given the function \(f(x)= x^{2} - 2x - 8\), find
the intervals where \(f\)
is a decreasing function.
\(\left (-\infty ;1\right )\)
\(\left (-\infty ;8\right )\)
\(\left (-\infty ;2\right )\)
\(\left (-\infty ;4\right )\)
9000070403
Level:
A
Given function \(f(x) = -x^{2} + 2x + 3\), find
the intervals where \(f\)
is an increasing function.
\(\left (-\infty ;1\right )\)
\(\left (-\infty ;2\right )\)
\(\left (-\infty ;3\right )\)
\(\left (-\infty ;6\right )\)
9000070404
Level:
A
Given function \(f(x)= -x^{2} + 4x + 12\), find
the intervals where \(f\)
is a decreasing function.
\(\left (2;\infty \right )\)
\(\left (1;\infty \right )\)
\(\left (-4;\infty \right )\)
\(\left (-6;\infty \right )\)
9000070405
Level:
A
Given function \(f(x)= x^{3} + 3x^{2} - 24x + 5\), find
the intervals where \(f\)
is a decreasing function.
\(\left (-4;2\right )\)
\(\left (-3;5\right )\)
\(\left (-3;3\right )\)
\(\left (-5;1\right )\)