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

Maneesha Reddy , 9 Years ago
Grade 12th pass
anser 1 Answers
Anoopam Mishra

Last Activity: 9 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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