Applications of derivatives

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 \( x=0 \)

2010020001

Level: 
A
A function \(f\) is given by the formula \(f(x)=1+\sqrt{\frac{x^4}{4}-2x^2+4}\). Choose the true statement about local extrema of this function.
The function has two local minima and one local maximum.
The function has two local maxima and one local minimum.
The function has two local minima and no local maximum.
The function has two local maxima and no local minimum.

2010020002

Level: 
A
A function \(f\) is given by the formula \(f(x)=1-\sqrt{\frac{x^4}{4}-4x^2+16}\). Choose the true statement about local extrema of this function.
The function has two local maxima and one local minimum.
The function has two local minima and one local maximum.
The function has two local minima and no local maximum.
The function has two local maxima and no local minimum.