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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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