Applications Of Derivatives Question 391
Question: The least value of the sum of any positive real number and its reciprocal is
[MP PET 1994]
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)=x+\frac{1}{x}\Rightarrow f’(x)=1-\frac{1}{x^{2}} $
therefore $ f’(x)=0\Rightarrow x^{2}-1=0\Rightarrow x=1,-1 $
But given that x is positive,
Hence at $ x=1,f(x)=1+\frac{1}{1}=2 $ .
BETA
