Applications Of Derivatives Question 232
Question: The minimum value of $ [(5+x)(2+x)]/[1+x] $ for non-negative real x is [Kurukshetra CEE 1998]
Options:
A) 12
B) 1
C) 9
D) 8
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ f(x)=\frac{[(5+x)(2+x)]}{[1+x]} $
$ f(x)=1+\frac{4}{1+x}+(5+x)=(6+x)+\frac{4}{(1+x)} $
therefore $ f’(x)=1-\frac{4}{{{(1+x)}^{2}}}=0 $ ; $ x^{2}+2x-3=0 $
therefore $ x=-3,\ 1 $ Now $ {f}’’,(x)=\frac{8}{{{(1+x)}^{3}}} $ , $ {f}’’,(-3)=-ve $ , $ {f}’’,(1)=+ve $
Hence minimum value at $ x=1 $
$ f(1)=\frac{(5+1)(2+1)}{(1+1)}=\frac{6\times 3}{2}=9 $ .
BETA
