Question
If f(x)= x, g(x)= 2 x, h(x)= 3 x and I(x) = x, then which of the following option is correct?
BITSAT
Mathematics
Application of Derivatives
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Mathematics Question (2023) — Solution
Options
- A. f(x) and g(x) are strictly decreasing in (0, / 2)
- B. h(x) is neither increasing nor decreasing in (0, / 2)
- C. I ( x ) is strictly increasing in (0, / 2)
- D. All are correct
Answer
D. All are correct
Step-by-step solution
(a) Let f(x)= x, then f^ (x)=- x. In interval (0, 2 ), f^ (x) Therefore, f(x) is strictly decreasing on (0, 2 ) (b) Let f(x)= 2 x f^ (x)=-2 x 2 x In interval (0, 2 ), f^ (x) Because 2 x will either lie in the first or second quadrant which will give a positive value. Therefore, f(x) is strictly decreasing on (0, 2 ) (c) Let f^ (x)= 3 x f ^ ( x )=-3 3 x . In Interval (0, 3 ), f ^ ( x ) Because 3 x will either lie in the first or second quadrant which will give a positive value. Therefore, f ( x ) irstrictly decreasing on (0, 3 ). When x ( 3 , 2 ), then f ^ ( x )>0 Because 3 x will lie in the third quadrant. Therefore, f(x) is not strictly decreasing on (0, 2 ) (d) Let f(x)= x f^ (x)= ^2 x. In Interval x (0, 2 ), f ^ ( x )>0 Therefore, f(x) is not strictly decreasing on (0, 2 )
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