Analyzing function behavior

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 \( x_2=4 \)

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 \( x=3 \)

1103163609

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 maximum at \( x=0 \)
local minimum at \( x=3 \), local maximum at \( x=0 \)
local minimum at \( x=1 \), local maximum at \( x=3 \)
local minimum at \( x=0 \), local maximum at \( x=3 \)
local minimum at \( x=0 \)

2010012505

Level: 
A
Identify a true statement about the function \(f(x) = -\frac{3} {4}x^{4} +2x^{3}\).
The function \(f\) has a local maximum at \(x = 2\).
The function \(f\) has a local minimum at \(x = 0\).
The function \(f\) has two local extrema. These extrema are at \(x = 0\) and \(x = 2\).
The function \(f\) has neither local minimum nor local maximum.