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sinx+a^2x+b is increasing for all x,then a belongs to

sinx+a^2x+b is increasing for all x,then a belongs to

Grade:12th pass

1 Answers

Anoopam Mishra
126 Points
8 years ago
f(x) = sin x + ax^2 + b
f`(x) = cosx + 2ax \geqslant 0 Here we cannot solve for x easily.
f``(x) = -sinx + 2a \geqslant 0
=>2a \geqslant sinx
sinx \ \epsilon \ [-1,1] 
=> 2a \geqslant 1
=> a \geqslant \frac{1}{2}

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