Question
The function f(x)= (1+x)- 2 x 2+x is increasing on
BITSAT
Mathematics
Application of Derivatives
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Mathematics Question (2023) — Solution
Options
- A. (0, )
- B. (- , 0)
- C. (- , )
- D. None of these
Answer
A. (0, )
Step-by-step solution
Given f(x)= (1+x)- 2 x 2+x aligned & f^ (x)= 1 1+x - (2+x)(2)-2 x (2+x)^2 \\ & = 1 1+x - 4 (2+x)^2 \\ & = (2+x)^2-4-4 x (1+x)(2+x)^2 = x^2 (1+x)(2+x)^2 >0 for all \\ & x (0, ) aligned Thus, given function f ( x ) is increasing on (0, ).
Related: Mathematics — Application of Derivatives · All PYQ Banks