find the maximum and minimum value of f (x)=x^50-x^20 in tge interval (0, pi/2)

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We have,fx=x50-x20 , x0,π2f'x=50x49-20x19=10x195x30-2For maxima or minima f'x=010x195x30-2=0Either x19=0or  5x30-2=0when  x19=0x=0 but x0,π2, hence x=0 will not be considered.When 5x30-2=0x30=25=0.4x=0.4130As f'x=10x195x30-2 Now f'x>0 when x>0.4130 i.e. f'x increasesand f'x<0 when x<0.4130i.e. f'x decreases,hence f'x will have point of local minima at x=0.4130.fx=x50-x20=x20x30-1f0.4130=0.420300.43030-1=0.4230.4-1=0.423-0.6fxmin=-0.60.423 AnswerHere maximum value cannot be determined as we do not know number just before x=π2.But we can say that maximum value tends towards fπ2fx=x20x30-1fxmaxπ220π230-1 Answer

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