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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