Question
Consider the function f(x)=|x-1| /x^ 2 , then f(x) is
BITSAT
Mathematics
Application of Derivatives
2020
BITSAT 2020
BITSAT Mathematics Question (2020) — Solution
Options
- A. increasing in (0,1) (2, )
- B. increasing in (- , 0) (1,2)
- C. decreasing in (0,1) (2, )
- D. decreasing in (0,1) (2, )
Answer
D. decreasing in (0,1) (2, )
Step-by-step solution
f(x)= |x-1| x^ 2 = \ array l 1-x x^ 2 , x 1 array . Clearly, f(x) is continuous for all x R except at x=0 f^ (x)= \ array l x-2 x^ 3 , x 1 array . f^ (x)>0 x 2 Hence, f(x) is increasing in (- , 0) (1,2) and decreasing in (0,1) (2, ).
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