What are the critical points of # f(x,y)=x^3 y + 4x^2 − 8y#? Calculus Graphing with the First Derivative Identifying Stationary Points (Critical Points) for a Function 1 Answer Jim H Nov 14, 2016 #(2, -4/3)# Explanation: #f_x(x,y) = 3x^2y+8x# #f_y(x,y) = x^3-8# Solve: #3x^2y+8x = 0# #x^3-8 = 0# #" "# so #x=2# now substitute in the other equation to get #12y+16 = 0# #" "# so #y=-4/3# 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 2269 views around the world You can reuse this answer Creative Commons License