9000070302
Level:
B
Given function \(f(x) = x^{3} + 3x^{2} + 12x + 4\), find
the intervals where \(f\)
is a strictly concave down function.
\((-\infty ,-1)\)
\((-\infty ,0)\)
\((-\infty ,2)\)
\((-\infty ,4)\)
Function Behavior
9000070303
Level:
B
Given function \(f(x) = -x^{3} + 6x^{2} + 6x + 1\), find
the intervals where \(f\)
is a strictly concave up function.
\((-\infty ,2)\)
\((-1,\infty )\)
\((-\infty ,3)\)
\((-\infty ,6)\)
9000070304
Level:
B
Given function \(f(x) = -x^{3} - 12x^{2} + 12x - 2\), find
the intervals where \(f\)
is a strictly concave up function.
\((-\infty ,-4)\)
\((-\infty ,2)\)
\((-\infty ,6)\)
\((-\infty ,12)\)
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.
\(\left (-\infty ,1\right )\)
\(\left (-\infty ,8\right )\)
\(\left (-\infty ,2\right )\)
\(\left (-\infty ,4\right )\)
9000062406
Level:
C
Identify an asymptote to the graph of the following function.
\[
f(x) = \frac{x^{2} + 4}
{x}
\]
\(y = x\)
\(y = x + 1\)
\(y = x - 1\)
\(y = -x\)