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let f(x)=ax^3 + bx^2 + cx + dsinx.Find d condition dat f(x) is always one-one function.

3 years ago

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Dear MAnuj,


 f(x)= ax3+ bx2+ cx+dsinx


d f (x)/dx=3ax^2 + 2bx + c + dcosx <0 (say)


i.e. 3ax^2 + 2bx + c + d<0   (as max. of cosx =1)


and b^2 -4ac<0 (for im roots)


u get : b^2 < 3a(c+d)


but if u hd taken 3ax^2 + 2bx + c + dcosx >0


then take 3ax^2 + 2bx + c - d>0 



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3 years ago

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