Let the function f: (0, ) R be defined by f( ) = ( + )^2 + ( - )^4. Suppose the function f has a local minimum at precisely when _1 , , _r , where 0 < _1 < < _r < 1. Then the value of _1 + + _r is _____

JEE Advanced 2020 Mathematics question

Let the function be defined by

f(θ) = (θ + θ + (θ - θ.

Suppose the function has a local minimum at precisely when , where . Then the value of is

Answer: 0.5

With : and , so . , which vanishes when or

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Question ID VK-033839