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Quiz 11
You scored 100 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) ​4
b) ​3
c) ​1
d) ​2
e) ​5
Question 2
Your answer is CORRECT.
Determine if Rolles Theorem applies to the function ​f(x)=3cos(x)​ on ​[0,π]​. If so, ​find​ all
numbers ​c​ on the interval that satisfy the theorem.
a) ​c=π and 2π
b) ​c=π8 and 3π8
c) ​c=π2 and 3π2
d) ​Rolles Theorem does not apply to this function on the given interval.
e) ​c=π8,3π8,5π8 and 7π8
Question 3
Your answer is CORRECT.
Determine if the function ​f(x)=3x−−√−2x​ satisfies the Mean Value Theorem on [4, 49]. If so,
find all numbers ​c​ on the interval that satisfy the theorem.
a) ​c=812
b) ​The Mean Value Theorem does not apply to this function on the given interval.
c) ​c=818
d) ​c=814
e) ​c=−814
Question 4
Your answer is CORRECT.
Find the ​x​-value(s) where ​f​′​(x)=0​ given f​ (x)=−13x​3​+4x+2​.
a) ​x=0
b) ​x={−2,2}
c) ​x=−2
d) ​x=2
e) ​x={−2,0,2}
Question 5
Your answer is CORRECT.
Find the intervals on which ​f(x)=6x​4​+2x​3​ increases.
a) ​(−14,0)∪(0,∞)
b) ​(−∞,−14)
c) ​(0,∞)
d) ​(−∞,−14)∪(0,14)
e) ​(−∞,∞)
Question 6
Your answer is CORRECT.
Find the intervals on which ​f(x)=4xx​2​+16​ decreases.
a) ​(−∞,−4)∪(4,∞)
b) ​(−4,4)
c) ​(−∞,∞)
d) ​(4,∞)
e) ​(−∞,−4)∪(0,4)
Question 7
Your answer is CORRECT.
Find the intervals on which ​f(x)=4x​2​+94x​2​−9​ decreases.
a) ​(−∞,−32)∪(−32,0)
b) ​((−∞,−32)∪(32,∞)
c) ​(−∞,−32)∪(32,∞)
d) ​(−∞,∞)
e) ​(0,32)∪(32,∞)
Question 8
Your answer is CORRECT.
Find the intervals on which ​f(x)=2x​2​(14+x)​2​ decreases.
a) ​(7,∞)
b) ​(−14,−7)∪(0,∞)
c) ​(−∞,∞)
d) ​(−∞,−14)∪(−7,0)
e) ​(−∞,−14)∪(7,∞)
Question 9
Your answer is CORRECT.
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)=9cos​4​(x)​ decreases for ​0≤x≤π​.
a) ​f(x)​ is never decreases on the given interval.
b) ​[π4,3π4]
c) ​[π2,π]
d) ​[0,π]
e) ​[0,π2]