Analyzing function behavior

1103163608

Level: 
A
The graph of \( f' \) is given in the figure. Find the local extrema of \( f \). (The function \( f' \) is the derivative of the function \( f \).)
local minimum at \( x=3 \)
local minimum at \( x=2 \), local maximum at \( x=0 \)
local minimum at \( x=3 \), local maximum at \( x=0 \)
local minimum at \( x=0 \), local maximum at \( x=3 \)
local maximum at \( x=3 \)

1103163607

Level: 
A
The graph of \( f' \) is given in the figure. Find the local extrema of \( f \). (The function \( f' \) is the derivative of the function \( f \).)
local minima at \( x_1=-1 \) and \( x_2=4 \), local maximum at \( x=1 \)
local minimum at \( x=3 \), local maximum at \( x=0 \)
local minimum at \( x=-1 \), local maximum at \( x=4 \)
local minima at \( x_1=-1 \) and \( x_2=1 \), local maximum at \( x=4 \)
local minimum at \( x=1 \), local maxima at \( x_1=-1 \) and \( x_2=4 \)

1103163606

Level: 
A
The graph of \( f' \) is given in the figure. Find the local extrema of \( f \). (The function \( f' \) is the derivative of the function \( f \).)
local minimum at \( x=0 \), local maxima at \( x_1=-2 \) and \( x_2=3 \)
local minimum at \( x=-1 \), local maximum at \( x=2 \)
local minima at \( x_1=-2 \) and \( x_2=3 \), local maximum at \( x=0 \)
local minima at \( x_1=-2 \) and \( x_2=0 \), local maximum at \( x=3 \)
local minimum at \( x=-2 \), local maxima at \( x_1=0 \) and \( x_2=2 \)

9000142001

Level: 
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-1;0)\) and \((1;\infty )\), concave down on \((-\infty ;-1)\) and \((0;1)\), inflection at \(x = 0\)
concave up on \((-\infty ;-1)\) and \((0;1)\), concave down on \((-1;0)\) and \((1;\infty )\), inflection at \(x = 0\)
concave up on \((-1;0)\) and \((1;\infty )\), concave down on \((-\infty ;-1)\) and \((0;1)\), no inflection
concave up on \((-1;0)\cup (1;\infty )\), concave down on \((-\infty ;-1)\cup (0;1)\), inflection at \(x = 0\)

9000142002

Level: 
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ;1)\), concave down on \((1;\infty )\), inflection at \(x = 1\)
concave up on \((1;\infty )\), concave down on \((-\infty ;1)\), inflection at \(x = 1\)
concave up on \((-\infty ;0)\), concave down on \((0;\infty )\), inflection at \(x = 0\)
concave up on \((-\infty ;1)\), concave down on \((1;\infty )\), inflection at \(x = \frac{2} {3}\)

9000142003

Level: 
B
Identify a correct statement related to the function $f$ shown in the picture.
concave up on \((-\infty ;0)\) and \((1;\infty )\), concave down on \((0;1)\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)
concave up on \((-\infty ;0)\cup (1;\infty )\), concave down on \((0;1)\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)
concave up on \((0;1)\), concave down on \((-\infty ;0)\) and \((1;\infty )\), inflection at \(x_{1} = 0\) and \(x_{2} = 1\)
concave up on \((-\infty ;0)\) and \((1;\infty )\), concave down on \((0;1)\), a unique inflection at \(x = 0\)