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 $f$).
Analyzing function behavior
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 $f$).
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 $f$).
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 $f$).
1103163505
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 $f$).
2010013905
Level:
B
Suppose a function is concave down on the interval \([-1;2]\). Which one of the offered functions has that property?
\(g(x)=\sqrt{-2x+8}\)
\(f(x)=\frac{-x+2}{(x+3)^2}\)
\(h(x)=\frac{x^2-1}{x}\)
\(k(x)=\frac12x^3+3x^2-x+2\)
2010013906
Level:
B
Suppose a function is convex up on the interval \([-2;1]\). Which one of the offered functions has that property?
\(h(x)=-\sqrt{x+5}\)
\(f(x)=\frac{x-2}{(x+5)^2}\)
\(g(x)=\frac{x^2-2}{2x}\)
\(k(x)=-\frac15x^3-2x^2+x+1\)
2010013907
Level:
B
How many of the given functions have exactly one inflection point?
\[\]
\(f(x)=(x+2)^5+(2+x)^3-2,\) \(g(x)=\frac1{6(x+4)^4},\) \(h(x)=\frac{x^3+2x^2+x+2}{x}\)
2
1
3
None of these functions has exactly one inflection point.
2010013908
Level:
B
How many of the given functions have exactly one inflection point?
\[\]
\(f(x)=\frac1{-2(x+4)^4}+6,\) \(g(x)=-(x-3)^5-(-3+x)^3+1,\) \(h(x)=\frac{x^3-3x^2+6x+9}{-3x}\)
2
1
3
None of these functions has exactly one inflection point.
2110012503
Level:
B
Choose the graph of a function $f$ that satisfies
\begin{gather*}
f'(-2)=f'(0)=0; \\
f''(-2) < 0;\ f''(0) > 0
\end{gather*}
($f'$ is the derivative of the function $f$, $f''$ is the second derivative of the function $f$).
