Is #f(x)=1-xe^(-3x)# concave or convex at #x=-2#?

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Answer 1 · 2018-07-27T21:41:15

function is convex at #x=-2#

Given function:

#f(x)=1-xe^{-3x}#

#f'(x)=-x(-3e^{-3x})-e^{-3x}(1)#

#f'(x)=e^{-3x}(3x-1)#

#f''(x)=e^{-3x}(3)+(3x-1)(-3e^{-3x})#

#f''(x)=e^{-3x}(6-9x)#

#f''(-2)=e^{6}(6-9(-2))#

#=24e^{6}#

Since #f(-2)>0# hence the given function is convex at #x=-2#