Find interval of function, Mathematics

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Find interval for which the function f(x)=xex(1-x)  is increasing or decreasing function


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Sin[cot-1{cos(tan-1x)}], sin (cot -1 {cos (tan -1 x)}) tan -1 x = A  ...

sin (cot -1 {cos (tan -1 x)}) tan -1 x = A  => tan A =x sec A = √(1+x 2 ) ==>  cos A = 1/√(1+x 2 )    so   A =  cos -1 (1/√(1+x 2 )) sin (cot -1 {cos (tan -1 x)}) = s

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Sona

3/29/2013 6:33:44 AM

Differentiate the given equation

you get e^x(1-x) + (xe^x(1-x))*(1-2x)

this can be written as (e^x(1-x) )*[1+x - 2x^2]

this equation is +ve if 1+x - 2x^2) is >0

this equation is positive in (-ve infinity to -1/2)....union  ......(1 to +ve infinity)

 

 

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