Q23 of 137 Page 19

#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.

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