Question #12f8c Calculus Graphing with the First Derivative Identifying Stationary Points (Critical Points) for a Function 1 Answer Jim H Apr 7, 2017 #pi/3#. #pi#, and #(5pi)/3#, if you meant to leave out the #0#. If you want all the critical numbers on a full period, then include #0# or #2pi#. Explanation: #f'(x) = 2sinxcosx-sinx = sinx(2cosx-1)# #f'(x) is nevern undefined and #f'(x) = 0# at #sinx = 0# or #cosx = 1/2#. This leads to solutions #x=0#, #x=pi#, #x=pi/3# and #x=(5pi)/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 1959 views around the world You can reuse this answer Creative Commons License