Q3 of 137 Page 19

How should we choose two numbers, each greater than or equal to –2, whose sum is 1/2 so that the sum of the first and the cube of the second is minimum?

Let a and b be two numbers such that a, b ≥ - 2


Given: a + b =


Assume, S = a + b3


S = a + ( - a)3


= 1 + 3( - a)2( - 1)


Condition maxima and minima is









For S to minimum,



Hence, and


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