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Find the values of x where function f(X...

Find the values of x where function `f(X) = (sin x + cosx)(e^(x))` in `(0,2pi)` has point of inflection

Text Solution

Verified by Experts

The correct Answer is:
`x=pi//4,5pi//4`
We have f(x) =`(sinx+cosx)^(e^(x)`
`therefore f(x) =(sinx+cosx)e^(x)+e^(x)(cosx-sinx)`
`rarr f(x) =2e^(x)cosx`
`f''(x) =2(e^(x) cosx-=e^(x)sinx)`
`=2e^(x)(cosx-sinx)`
If f''(x) =0 then cos x - sinx =0
`therefore tanx=1 rarr x =(pi)/(4),(5pi)/(4)`
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