isi-entrance 2012 Q18

isi-entrance · India · solved Stationary points and optimisation Find absolute extrema on a closed interval or domain

If $xy = 1$, find the minimum value of $\dfrac{4}{4-x^2} + \dfrac{9}{9-y^2}$.

Setting $y = 1/x$ and simplifying, the minimum occurs at $x^2 = 2/3$, giving the minimum value $12/5$. (B)

If $xy = 1$, find the minimum value of $\dfrac{4}{4-x^2} + \dfrac{9}{9-y^2}$.