Determining Concavity/Inflection Points
Determining the Extremas
Analyzing the First Derivative
Determining Increasing and Decreasing
Overall
100
Given the graph of the function f below, determine all intervals where f(x) is concave up on the open interval (−9,9).
What is (-4,0) and (5,9)?
100
The relative maximum value within the closed interval [-1,5].
What is 5?
100
Given the graph of the function f below, determine all values of x on the open interval (−9,9) where f′(x) goes from negative to positive.
What is -5 and 5?
100
Given the function f(x)=-2x4+8x3, determine all intervals on which f′ is increasing.
What is [0,1]?
100
Given selected values of the twice-differentiable function f, which of the following choices could possibly be true on the entire domain 0≤x≤6?
A.f′(x)<0 and f′(x)<0
B.f′(x)>0 and f′(x)<0
C.f′(x)>0 and f′(x)>0
D.f′(x)<0 and f′(x)>0
What is C?
200
Given the graph of the function f below, determine all intervals where f(x) is concave up on the open interval (−9,9).
What is (-6,-4) and (1,6)?
200
The relative minimum value on the closed interval [-2,6]
What is -2?
200
Given the graph of the function f below, determine all intervals on the open interval (−9,9) where f′(x)<0 and f(x)<0.
What is (-3,4)?
200
Given the function f(x)=x4-8x3 determine all intervals on which f is increasing.
What is [6,∞)?
200
Fill in the Blanks.
What is
300
Given the function
-1/15 x^6+6x^4
, find all intervals on which f is concave up.
What is (-6, 6)?
300
Given the function f(x)=x4-4x3-4, determine the absolute minimum value of f on the closed interval [-1, 4].
What is -31?
300
Find all intervals on which f(x) is decreasing.
-2x^3 +27x^2-19
What is (-∞,0) and (9,∞)?
300
Given the function f'(x)=-x4+20x3-36x2 determine all intervals on which f is increasing.
What is [2,18]?
300
Given the function
f(x)=\frac{1}{6}x^6+x^5-5x^4
find all x-values where ff has an inflection point.
What is -6 and 2?
400
Given the function
-1/5 x^5-x^4
, find all intervals on which ff is concave down.
What is (-3,∞)?
400
Given the function f(x)=-x3-3x2-2 determine the absolute minimum value of f on the closed interval [-4, 3].
What is -56?
400
Find the x-coordinates of all relative maxima of f(x).
f(x)=\frac{2}{5}x^5+5x^4+16x^3-15
What is -6?
400
Given the function f(x)=-2x5+20x4, determine all intervals on which f is decreasing.
What is (-∞,0] and [8,∞)?
400
Find all values of xx where the function
xe^(-x-3)
has a relative maximum.
What is 1?
500
Given the function
-3/5 x^5+7x^4
, find all intervals on which f is concave up.
What is (-∞,7)?
500
Given the function f(x)=-x4+12x3-16x2+7, determine the absolute minimum value of f on the closed interval [-2, 3].
What is -169?
500
Find the x-coordinates of all relative minima of f(x).
f(x)=−2x^3 −27x^2 −84x−3
What is -7?
500
Given the function f(x)=-2x3+24x2-72x determine all intervals on which f′ is decreasing.
What is [4,∞)?
500
Find all values of x where the function has a relative extrema.
(e^-2x)/(x+4)
What is
-9/2