What are the points of inflection of #f(x)=x^{2}e^{11 x} #?

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Answer 1 · 2016-10-02T16:33:23

#x = +-sqrt(2/11)-2/11#.

Sufficient condition for giving points of inflexion, if any#:r

f''=0 and f''' is not 0.

Here,

#f'=2xe^(11x)+11x^2e^(11x)=e^(11x)(11x^2+2x)#

#f''=e^(11x)(121x^2+44x+2)#

#f'''=e^(11x)(1331x^2+726x+66)#

f''=0 gives

#x=+-sqrt(2/11)-2/11#

and #f'''(+-sqrt(2/11)-2/11)# are not 0.

So, the points of inflexion are #x =+-sqrt(2/11)-2/11#