Consider f(x)=xe^{-kx} for k>0. Find the relative extrema and the

Globokim8

Globokim8

Answered question

2021-10-05

Consider f(x)=xekx for k>0. Find the relative extrema and the points of inflection of the function.

Answer & Explanation

jlo2niT

jlo2niT

Skilled2021-10-06Added 96 answers

Step 1
f(x)=xekx
For finding relative extrema we need to us first derivative test
Now for that
f(x)=0 here
f(x)=(kx1)ekx
0=(kx1)ekx
let k=2
0=(2x1)e2x
x=0.5 is a critical point
f(x) in domain (, 0.5), (0.5, )
min={(0.5, 1e0.5})

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