What are the critical numbers of #f(x) = x^2*(1 + 3 ln x)#? Calculus Graphing with the First Derivative Identifying Stationary Points (Critical Points) for a Function 1 Answer Jim H Mar 17, 2017 The only critical number is #x = e^(-5/6)# Explanation: #f'(x) = 2x(1+3lnx)+x^2(3/x)= x(6lnx+5)# #f'(x)# is defined for all #x# in the domain of #f# and #f'(x)=0# at #lnx = -5/6# so #x = e^(-5/6)#. Answer link Related questions How do you find the stationary points of a curve? How do you find the stationary points of a function? How many stationary points can a cubic function have? How do you find the stationary points of the function #y=x^2+6x+1#? How do you find the stationary points of the function #y=cos(x)#? How do I find all the critical points of #f(x)=(x-1)^2#? Let #h(x) = e^(-x) + kx#, where #k# is any constant. For what value(s) of #k# does #h# have... How do you find the critical points for #f(x)=8x^3+2x^2-5x+3#? How do you find values of k for which there are no critical points if #h(x)=e^(-x)+kx# where k... How do you determine critical points for any polynomial? See all questions in Identifying Stationary Points (Critical Points) for a Function Impact of this question 1272 views around the world You can reuse this answer Creative Commons License