PRINTABLE VERSION
Quiz 11
You scored 60 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) ​1
b) ​3
c) ​5
d) ​2
e) ​4
Question 2
Your answer is INCORRECT.
Determine if Rolles Theorem applies to the function ​f(x)=x​3​−x​ on ​[−1,0]​. If so, ​find​ all numbers
c​ on the interval that satisfy the theorem.
a) ​c=3–√3
b) ​c=3–√3 and c=−3–√3
c) ​c=−1
d) ​Rolles Theorem does not apply to this function on the given interval.
e) ​c=−3–√3
Question 3
Your answer is INCORRECT.
Determine if the function ​f(x)=516−x​2​−−−−−−√​ satisfies the Mean Value Theorem on [0, 4]. If
so, find all numbers ​c​ on the interval that satisfy the theorem.
a) ​c=22–√
b) ​c=−22–√
c) ​c=−22–√ and 22–√
d) ​The Mean Value Theorem does not apply to this function on the given interval.
e) ​c=0
Question 4
Your answer is CORRECT.
The graph of ​f(x)​ is shown. Find the ​x​-value(s) where f​ ​′​(x)=0​.
a) ​x={−5,5}
b) ​x=−5
c) ​x=0
d) ​x={−5,0,5}
e) ​x=5
Question 5
Your answer is CORRECT.
Find the intervals on which ​f(x)=5x​4​+3x​3​ increases.
a) ​(−∞,−920)
b) ​(−∞,∞)
c) ​(0,∞)
d) ​(−920,0)∪(0,∞)
e) ​(−∞,−920)∪(0,920)
Question 6
Your answer is CORRECT.
Find the intervals on which ​f(x)=6xx​2​+25​ decreases.
a) ​(−∞,−5)∪(0,5)
b) ​(−∞,−5)∪(5,∞)
c) ​(5,∞)
d) ​(−5,5)
e) ​(−∞,∞)
Question 7
Your answer is CORRECT.
Find the intervals on which ​f(x)=x​2​+1x​2​−1​ increases.
a) ​(−∞,−1)∪(−1,0)
b) ​(−∞,∞)
c) ​(−∞,−1)∪(1,∞)
d) ​(0,1)∪(1,∞)
e) ​((−∞,−1)∪(1,∞)
Question 8
Your answer is CORRECT.
Find the intervals on which ​f(x)=2x​2​(10+x)​2​ decreases.
a) ​(−∞,−10)∪(−5,0)
b) ​(−10,−5)∪(0,∞)
c) ​(−∞,−10)∪(5,∞)
d) ​(5,∞)
e) ​(−∞,∞)
Question 9
Your answer is INCORRECT.
Find the intervals on which ​f(x)=5x+5cos(x)​ increases for ​0≤x≤2π​.
a) ​[0,2π]
b) ​[π2,2π]
c) ​f(x)​ is never increasing on the given interval.
d) ​[0,3π2]
e) ​[3π2,2π]
Question 10
Your answer is INCORRECT.
Find the intervals on which ​f(x)=2cos​4​(x)​ decreases for ​0≤x≤π​.
a) ​[π4,3π4]
b) ​f(x)​ is never decreases on the given interval.
c) ​[π2,π]
d) ​[0,π]
e) ​[0,π2]