9000079107
Level:
A
What is the function value of the function $f$ at its local minimum?
\[
f(x) = \frac{2}
{\sqrt{4x - x^{2}}}
\]
\(1\)
\(2\)
\(0\)
the local minimum does not exist
Function Behavior
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.
\((-\infty ;2)\)
\((-1;\infty )\)
\((-\infty ;3)\)
\((-\infty ;6)\)
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.
\((-4;1)\)
\((-6;2)\)
\((2;4)\)
\((-5;4)\)