JEE Advanced 2020 Full Test 2 Paper 1

Question : 44 of 54

Marks: +1, -0

Which of the following is/are true?

If y=f(x) is a strictly monotonic function in (a,b) with f(x)≠0, then the area bounded by y=f(x), the lines x=a,x=b and y=f(c) where c∈(a,b) is minimum when c=‌
a+b
2
y=f(x) is a strictly monotonic function in (a,b) with f(x)≠0, then the area bounded by the lines x=a,x=b and y=f(c) where c∈(a,b) is minimum when c=‌
2a+b
3
or c=‌
a+2b
3
.
If the area bounded by f(x)=‌
x2
3
−x2 and the lines x=0,x=2 and the x -axis is minimum when a=‌
2
3
If the area bounded by f(x)=‌
x3
3
−x2 and the lines x=0,x=2 and the x -axis is minimum when a=‌
28
81

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