What are the points of inflection, if any, of #f(x)=x^4-x^2+5 #?

1 Answer
Dec 24, 2015

Inclection points are #(sqrt6/6,187/36)# and #(-sqrt6/6,187/36)#.

Explanation:

#color(white)xxf(x)=x^4-x^2+5#

#=>d/dx[f(x)]=4x^3-2x#
#=>d^2/dx^2[f(x)]=12x^2-2#

For #d^2/dx^2[f(x)]=0#,
#color(white)xx12x^2-2=0#

#=>x=+-sqrt6/6#

For #x=sqrt6/6#,
#color(white)xxy=color(red)((sqrt6/6))^4-color(red)((sqrt6/6))^2+5#
#color(white)(xxx)=1/6^2-1/6+5#
#color(white)(xxx)=187/36#

For #x=-sqrt6/6#,
#color(white)xxy=187/36#

Therefore inclection points are #(sqrt6/6,187/36)# and #(-sqrt6/6,187/36)#.

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