PRINTABLE VERSION
Quiz 11
You scored 80 out of 100
Question 1
Your answer is CORRECT.
The function ​f​ is graphed below on the ​interval​ [0,10].Give the ​number of values​c​ between 0
and 10 which satisfy the conclusion of the mean value theorem for ​f​.
a) ​5
b) ​1
c) ​4
d) ​3
e) ​2
Question 2
Your answer is CORRECT.
Determine if Rolles Theorem applies to the function ​f(x)=x​3​−x​ on ​[0,1]​. If so, find all numbers ​c
on the interval that satisfy the theorem.
a) ​c=1
b) ​c=−3–√3
c) ​c=−3–√3 and c=3–√3
d) ​Rolles Theorem does not apply to this function on the given interval.
e) ​c=3–√3
Question 3
Your answer is CORRECT.
Determine if the function ​f(x)=2x−−√−x​ satisfies the Mean Value Theorem on [1, 9]. If so, find
all numbers ​c​ on the interval that satisfy the theorem.
a) ​The Mean Value Theorem does not apply to this function on the given interval.
b) ​c=−4
c) ​c=4
d) ​c=8
e) ​c=2
Question 4
Your answer is CORRECT.
The graph of ​f(x)​ is shown. Find the ​x​-value(s) where f​ ​′​(x)=0​.
a) ​x=−5
b) ​x={−5,5}
c) ​x=5
d) ​x=0
e) ​x={−5,0,5}
Question 5
Your answer is CORRECT.
Find the intervals on which ​f(x)=x​3​−12x+7​ decreases.
a) ​(−∞,−2)∪(2,∞)
b) ​(2,∞)
c) ​(−∞,∞)
d) ​(−∞,−2)∪(0,2)
e) ​(−2,2)
Question 6
Your answer is CORRECT.
Find the intervals on which ​f(x)=5xx​2​+36​ decreases.
a) ​(−6,6)
b) ​(−∞,−6)∪(0,6)
c) ​(−∞,−6)∪(6,∞)
d) ​(−∞,∞)
e) ​(6,∞)
Question 7
Your answer is CORRECT.
Find the intervals on which ​f(x)=25x​2​+1625x​2​−16​ decreases.
a) ​(0,45)∪(45,∞)
b) ​(−∞,−45)∪(45,∞)
c) ​(−∞,∞)
d) ​((−∞,−45)∪(45,∞)
e) ​(−∞,−45)∪(−45,0)
Question 8
Your answer is CORRECT.
Find the intervals on which ​f(x)=4x​2​(8+x)​2​ increases.
a) ​(−∞,−8)∪(−4,0)
b) ​(−8,−4)∪(0,∞)
c) ​(4,∞)
d) ​(−∞,−8)∪(4,∞)
e) ​(−∞,∞)
Question 9
Your answer is INCORRECT.
Find the intervals on which ​f(x)=2x−2cos(x)​ increases for ​0≤x≤2π​.
a) ​[0,3π2]
b) ​[0,2π]
c) ​f(x)​ is never increasing on the given interval.
d) ​[3π2,2π]
e) ​[π2,2π]
Question 10
Your answer is INCORRECT.
Find the intervals on which ​f(x)=2cos​2​(x)​ decreases for ​0≤x≤π​.
a) ​f(x)​ is never decreases on the given interval.
b) ​[0,π]
c) ​[π4,3π4]
d) ​[0,π2]
e) ​[π2,π]