9000079104
Level:
A
Find the $x$ at which has the function $f$ a local minimum.
\[
f(x) = \frac{\ln x}
{x}
\]
does not exist
\(x = 0\)
\(x = 1\)
\(x =\mathrm{e}\)
Function Behavior
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.
\(\left (-3;0\right )\)
\(\left (-\infty ;-6\right )\)
\(\left (0;\infty \right )\)
\(\left (-3;4\right )\)
9000070301
Level:
B
Given function \(f(x)= x^{3} - 9x^{2} + 12x + 6\), find
the intervals where \(f\)
is a strictly concave down function.
\((-\infty ;3)\)
\((-\infty ;4)\)
\((-\infty ;6)\)
\((-\infty ;12)\)
9000070302
Level:
B
Given function \(f(x) = x^{3} + 3x^{2} + 12x + 4\), find
the intervals where \(f\)
is a strictly concave down function.
\((-\infty ;-1)\)
\((-\infty ;0)\)
\((-\infty ;2)\)
\((-\infty ;4)\)
9000070303
Level:
B
Given function \(f(x) = -x^{3} + 6x^{2} + 6x + 1\), find
the intervals where \(f\)
is a strictly concave up function.
\((-\infty ;2)\)
\((-1;\infty )\)
\((-\infty ;3)\)
\((-\infty ;6)\)