What are the points of inflections for #f(x) = (x^2) - 3/x^3#?

1 Answer
Jan 19, 2016

Point of inflection is #xapprox 1.783#

Explanation:

To find points of inflection of a function #f(x)# we need to find second derivative of #f(x)# and equate it to zero. Then find the roots of the polynomial thus obtained.
#f(x)=(x^2)-3/x^3#
or #f(x)=x^2-3x^-3#

First derivative #f'(x)=2x+9x^-4#
Second derivative #f''(x)=2-36x^-5#
For point of inflection #f''(x)=0#
#implies# #2-36x^-5=0#
#implies36x^-5=2#

Solving for #x#
Only root is #x=root(5)(36/2)#