The sum of two non-zero numbers is 8, the minimum value of the sum of their reciprocals is : A. 1/4 B. 1/2 C.1/8 D. none of these

Question

The sum of two non-zero numbers is 8, the minimum value of the sum of their reciprocals is :

A. \(\frac{1}{4}\)

B. \(\frac{1}{2}\)

C. \(\frac{1}{8}\)

D. none of these

Answer 1

Option : (B)

Let the two non zero numbers be x and y. 

So, 

x + y = 8 

y = 8 - x

And,

f(x,y) = \(\frac{1}{x}\) + \(\frac{1}{y}\)

Put y = 8-x in f(x,y)

Therefore it will become a function in f(x) = \(\frac{1}{x}\) + \(\frac{1}{(8-x)}\)

Hence by second derivative test 

f’’(x) > 0 so it’s a point of minimum.