9000070403
Level:
A
Given function \(f(x) = -x^{2} + 2x + 3\), find
the intervals where \(f\)
is an increasing function.
\(\left (-\infty ,1\right )\)
\(\left (-\infty ,2\right )\)
\(\left (-\infty ,3\right )\)
\(\left (-\infty ,6\right )\)
Function Behavior
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.
\(\left (-4,2\right )\)
\(\left (-3,5\right )\)
\(\left (-3,3\right )\)
\(\left (-5,1\right )\)
9000070406
Level:
A
Given function \(f(x)= x^{3} + 6x^{2} - 15x + 7\), find
the intervals where \(f\)
is an increasing function.
\(\left (-\infty ,-5\right )\)
\(\left (-\infty ,-3\right )\)
\(\left (-1,\infty \right )\)
\(\left (-3,\infty \right )\)
9000070407
Level:
A
Given the function \(f(x) = -x^{3} + 3x^{2} + 9x - 1\), find
the intervals where \(f\)
is a decreasing function.
\(\left (3,\infty \right )\)
\(\left (-\infty ,1\right )\)
\(\left (-1,3\right )\)
\(\left (1,\infty \right )\)
9000070408
Level:
A
Given the function \(f(x) = -x^{3} + 3x^{2} + 45x - 12\), find
the intervals where \(f\)
is an increasing function.
\(\left (-3,5\right )\)
\(\left (-\infty ,-3\right )\)
\(\left (5,\infty \right )\)
\(\left (-12,45\right )\)
9000070409
Level:
A
Given the function \(f(x) = \frac{x^{2}}
{x-2}\), find
the intervals where \(f\)
is a decreasing function.
\(\left (0,2\right )\)
\(\left (-\infty ,-1\right )\)
\(\left (5,\infty \right )\)
\(\left (2,5\right )\)
9000070410
Level:
A
Given the function \(f(x) = - \frac{x^{2}}
{x+3}\), find
the intervals where \(f\)
is an increasing function.
\(\left (-3,0\right )\)
\(\left (-\infty ,-6\right )\)
\(\left (0,\infty \right )\)
\(\left (-3,4\right )\)
9000079101
Level:
A
Find the intervals of monotonicity for the following function.
\[
f(x)= \frac{3x + 1}
{2x - 5}
\]
Decreasing on \(\left (-\infty , \frac{5}
{2}\right )\)
and \(\left (\frac{5}
{2},\infty \right )\).
Decreasing on \(\left (-\infty , \frac{5}
{2}\right )\cup \left (\frac{5}
{2},\infty \right )\).
Decreasing on \(\left (-\infty , \frac{5}
{2}\right )\),
increasing on \(\left (\frac{5}
{2},\infty \right )\).
Increasing on \(\left (-\infty , \frac{5}
{2}\right )\),
decreasing on \(\left (\frac{5}
{2},\infty \right )\).
9000079102
Level:
A
Find the intervals where the following function is a decreasing function.
\[
f(x) = \frac{x^{2} + 1}
{x}
\]
\([ - 1,0)\) and
\((0,1] \)
\([ - 1,1] \)
\((-\infty ,-1] \) and
\([1,\infty) \)
\([1,\infty) \)