9000070304
Level:
B
Given function \(f(x) = -x^{3} - 12x^{2} + 12x - 2\), find
the intervals where \(f\)
is a strictly concave up function.
\((-\infty ;-4)\)
\((-\infty ;2)\)
\((-\infty ;6)\)
\((-\infty ;12)\)
Analyzing function behavior
9000070305
Level:
B
Given function \(f(x) = x^{4} + 2x^{3} - 36x^{2} + 36x + 2\), find
the intervals where \(f\)
is a strictly concave down function.
\((-3;2)\)
\((-3;4)\)
\((-4;2)\)
\((-2;3)\)
9000070306
Level:
B
Given function \(f(x) = x^{4} + 6x^{3} - 24x^{2} + x + 3\), find
the intervals where \(f\)
is a strictly concave down function.
\((-4;1)\)
\((-6;2)\)
\((2;4)\)
\((-5;4)\)
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.
\(\left (2;\infty \right )\)
\(\left (1;\infty \right )\)
\(\left (-4;\infty \right )\)
\(\left (-6;\infty \right )\)
9000062406
Level:
C
Identify an asymptote to the graph of the following function.
\[
f(x) = \frac{x^{2} + 4}
{x}
\]
\(y = x\)
\(y = x + 1\)
\(y = x - 1\)
\(y = -x\)