Question 18

x and y are real numbers satisfying the conditions 2 < x < 3 and - 8 < y < -7. Which of the following expressions will have the least value?

Solution

$$xy^2$$ will have it's least value when y=-7 and x=2 and equals 98.
So $$xy^2>98$$

$$x^2y$$ will have it's least value when y=-8 and x=3 and equals -72.
So, $$x^2y > -72$$

$$5xy$$ will have it's least value when y=-8 and x=3 and equals -120
So, $$5xy > -120$$

So, of the three expressions, the least possible value is that of 5xy

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