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


2 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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2 years ago

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