2010001702
Level:
A
What is the function value of the function $f$ at its local maximum?
\[
f(x) = \frac
{\sqrt{6x-x^2}}{2}
\]
\(\frac{3}{2}\)
\(0\)
\(2\)
The local maximum does not exist.
Analyzing function behavior
2010001701
Level:
A
Find all the $x$ at which the function $f$ has local extrema.
\[
f(x)= -2\left (x^2 - 4\right )^{5}
\]
\(x=0\)
\(x_1=0\),
\(x_2=2\)
\(x_1=-2\),
\(x_2=2\)
\(x_1=- 2\),
\(x_2=0\),
\(x_3=2\)
Asymptotes of the Graph of a Function
Submitted by ladislav.foltyn on Sun, 05/05/2019 - 17:281103163505
Level:
B
Choose the graph of a function $f$ that satisfies
\begin{gather*}
f'(0) \text{ does not exist}; \\
f''(x) > 0 \text{ if } x < 0 ; \\
f''(x) > 0 \text{ if } x > 1; \\
f''(x) < 0 \text{ if } 0 < x < 1
\end{gather*}
($f'$ is the derivative of a function $f$, $f''$ is the second derivative of a function $f$).
1103163504
Level:
B
Choose the graph of a function $f$ that satisfies
\begin{gather*}
f'(0)=f'(3)=0; \\
f''(0)=0;\ f''(3) < 0
\end{gather*}
($f'$ is the derivative of a function $f$, $f''$ is the second derivative of a function $f$).
1103163503
Level:
B
Choose the graph of a function $f$ that satisfies
\begin{gather*}
f'(0)=f'(3)=0; \\
f''(0) < 0;\ f''(3) > 0
\end{gather*}
($f'$ is the derivative of the function $f$, $f''$ is the second derivative of the function $f$).
1103163502
Level:
B
Choose the graph of a function $f$ that satisfies
$$ f''(0) > 0;\ f''(3) < 0 $$
($f''$ is the second derivative of the function $f$).
1103163501
Level:
B
Choose the graph of a function $f$ which does not satisfy
$$ f''(0) > 0;\ f''(2) < 0 $$
($f''$ is the second derivative of the function $f$).
