#Mark the correct alternative in each of the following

Let x, y be two variables and x > 0, xy = 1, then minimum value of x + y is

xy=1, x>0, y>0

⇒

x+y=

Let

Differentiating f(x) with respect to x, we get

Also, differentiating f’(x) with respect to x, we get

For minima at x=c, f’(c)=0 and f’’(c)<0

⇒ or (Since x>0)

f’’(1)=2>0

Hence, x=1 is a point of minima for f(x) and f(1)=2 is the minimum value of f(x) for x>0.