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Letf'(sin x)lt0 and f''(sin x) gt0 forall x in (0,(pi)/(2)) and g(x) =f(sinx)+f(cosx) If x=4 is the only point of maxima in its neighborhood but x=3 is neither a point of maxima nor a point of minima then which of the following can be true? |
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Answer» `a lt 0, b gt 0` or `-9+12+a=3a+b or 2a+b=3` Also `f(4^(+)) or 4a+b=-b+6 r 2a+b=3` Thus f(x) is contnous for INFINITE values of a and b also `f(x)={{:(-2x+4,xlt3),(a,3ltxlt4),((-b)/(4),xgt4):}` For f(x) to be diffentiable `f(3^(-))=f(3^(+))` or `a=-2 and -(bb)/(4) =a=-2 or b=8` But these values do not SATISFY EQUATION (1) HENCE f(x) cannot be differentiable
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