PRINTABLE VERSION
Quiz 11
You scored 70 out of 100
Question 1
Your ​answer​ is INCORRECT.
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) ​3
b) ​1
c) ​5
d) ​2
e) ​4
Question 2
Your answer is INCORRECT.
Determine if Rolles Theorem applies to the function ​f(x)=−3sin(2x)​ on ​[0,2π]​. If so, ​find​ all
numbers ​c​ on the interval that satisfy the theorem.
a) ​c=π4 and 3π4
b) ​Rolles Theorem does not apply to this function on the given interval.
c) ​c=π and 2π
d) ​c=π2 and 3π2
e) ​c=π4,3π4,5π4 and 7π4
Question 3
Your answer is CORRECT.
Determine if the function ​f(x)=3x−−√−3x​ satisfies the Mean Value Theorem on [1, 16]. If so,
find all numbers ​c​ on the interval that satisfy the theorem.
a) ​c=252
b) ​c=−254
c) ​c=258
d) ​The Mean Value Theorem does not apply to this function on the given interval.
e) ​c=254
Question 4
Your answer is CORRECT.
Find the ​x​-value(s) where ​f​′​(x)=0​ given f​ (x)=13x​3​−9x+1​.
a) ​x={−3,3}
b) ​x=−3
c) ​x={−3,0,3}
d) ​x=3
e) ​x=0
Question 5
Your answer is CORRECT.
Find the intervals on which ​f(x)=x​3​−75x+3​ increases.
a) ​(−∞,−5)∪(5,∞)
b) ​(−5,5)
c) ​(−∞,∞)
d) ​(5,∞)
e) ​(−∞,−5)∪(0,5)
Question 6
Your answer is CORRECT.
Find the intervals on which ​f(x)=6xx​2​+4​ decreases.
a) ​(−∞,−2)∪(2,∞)
b) ​(−∞,∞)
c) ​(−∞,−2)∪(0,2)
d) ​(2,∞)
e) ​(−2,2)
Question 7
Your answer is CORRECT.
Find the intervals on which ​f(x)=25x​2​+1625x​2​−16​ increases.
a) ​(−∞,−45)∪(45,∞)
b) ​(−∞,∞)
c) ​(0,45)∪(45,∞)
d) ​(−∞,−45)∪(−45,0)
e) ​((−∞,−45)∪(45,∞)
Question 8
Your answer is CORRECT.
Find the intervals on which ​f(x)=4x​2​(12+x)​2​ decreases.
a) ​(−∞,∞)
b) ​(−12,−6)∪(0,∞)
c) ​(6,∞)
d) ​(−∞,−12)∪(−6,0)
e) ​(−∞,−12)∪(6,∞)
Question 9
Your answer is INCORRECT.
Find the intervals on which ​f(x)=8x+8cos(x)​ increases for ​0≤x≤2π​.
a) ​[0,3π2]
b) ​[0,2π]
c) ​[3π2,2π]
d) ​[π2,2π]
e) ​f(x)​ is never increasing on the given interval.
Question 10
Your answer is CORRECT.
Find the intervals on which ​f(x)=2cos​2​(x)​ increases for ​0≤x≤π​.
a) ​[0,π2]
b) ​[π2,π]
c) ​[π4,3π4]
d) ​f(x)​ is never increases on the given interval.
e) ​[0,π]