LT 19 Part 1
LT 19 Part 2
LT 19 Part 3
LT 19 Part 4
LT 19 Misc
100
Given selected values of the twice differentiable function f, which of the following choices could possibly be true on the entire domain 3≤x≤9?
A) f' is positive and decreasing
B) f' is negative and decreasing
C) f' is negative and increasing
D) f' is positive and decreasing
What is D) f' is positive and decreasing?
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 {-4,6}?
100
Given the function f(x)=x3-12x-10, determine the absolute maximum value of f on the closed interval [-3,3].
What is 6?
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 (-9,-7) or (-5,2) or (5,9)?
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' is negative and decreasing
B) f' is negative and increasing
C) f' is positive and decreasing
D) f' is positive and increasing
What is C) f' is positive and decreasing?
200
Given the function f(x)=-x3+18x2-81x, determine all intervals on which f' is increasing.
What is (−∞,6)?
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 [0,2]?
200
Given the function f(x)=-x4+8x3-10x2-5, determine the absolute maximum value of f on the closed interval [-1,3].
What is 40?
200
Given the function f(x)=(1/15)x6+x5+(25/6)x4, find all x-values where f has an inflection point.
What is no inflection points?
200
Given the function f(x)=-x3+12x+6, determine the absolute minimum value of f on the closed interval [-3, 3].
What is -10?
300
Given the function f'(x)=x3-18x2, determine all intervals on which f is decreasing.
What is (−∞,18]?
300
Find all values of x where the function f(x)=x2e-x has a relative maximum.
What is 2?
300
Given the function f(x)=-x4+8x3-10x2+3, determine the absolute minimum value of f on the closed interval [-1,3].
What is -16?
300
Given the function f(x)=(1/5)x5-x4-12x3, find all intervals on which f is concave up.
What is (-3,0) U (6,∞)?
300
Find all intervals on which the function f(x)=(-2x)/(e3x-2) is increasing.
What is x>1/3?
400
The graph of f', the derivative of f, is shown below. Determine the values of x, if any, at which the function f has a relative minimum on the interval (-9,9).
What is 8?
400
Find all intervals on which f(x) is decreasing. f(x)=(10/3)x3-31x2+12x-40.
What is 1/5≤x≤6?
400
Given the function f(x)=x3+9x2+27x+2, determine the absolute maximum of f on the closed interval [-4,-1].
What is -17?
400
Given the function f(x)=x4+8x3+18x2, determine all intervals on which f is both decreasing and concave up.
What is (-∞,-3) U (-1,0)?
400
Given the function f(x)=-2x4-8x3, determine all intervals on which f is both decreasing and concave up.
What is (-2,0)?
500
The graph of f', the derivative of the function f is shown below. Determine all intervals on which f is decreasing on the closed interval [-9,9].
What is [-8,-2]U[0,4]?
500
Find the x-coordinates of all relative minima of f(x). f(x)=x3-12x2-27x-26.
What is 9?
500
Given the function f(x)=-x4+8x2+6, determine the absolute minimum value of f on the closed interval [-3,1].
What is -3?
500
Given the function f(x)=x4-8x3+18x2, determine all intervals on which f is both increasing and concave down.
What is (1,3)?
500
Find all intervals on which f(x) is decreasing. f(x)=(-3/5)x5+9x4-32x3+49.
What is x≤4 or x≥8?