How do you find the critical points of #k'(x)=x^3-3x^2-18x+40#? Calculus Graphing with the First Derivative Identifying Stationary Points (Critical Points) for a Function 1 Answer Jeronimo May 12, 2018 #x_1 = 1- sqrt(7), x_2 = 1+ sqrt(7)# Explanation: If you want the critical points of #k'(x)#, you have to compute #k''(x)#. An easy calculation gives us #k''(x) = 3x^2 - 6x - 18.#You only have to solve #3x^2 - 6x - 18=0.# 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 1761 views around the world You can reuse this answer Creative Commons License