For what values of x is #f(x)=(x-1)(x-6)(x-2)# concave or convex? Calculus Graphing with the Second Derivative Analyzing Concavity of a Function 1 Answer Jim H Feb 20, 2017 See below. Explanation: #f(x) = (x-1)(x6)(x-2) = x^3-9x^2+20x-12# #f'(x) = 3x^2-18x+20# #f''(x) = 6x-18# #f''(x)# is negative for #x < 3#, so #f# is concave (or concave down) on #(-oo,3)#. #f''(x)# is positive for #3 < x#, so #f# is convex (or concave up) on #(3,oo)#. Answer link Related questions How do you determine the concavity of a quadratic function? How do you find the concavity of a rational function? What is the concavity of a linear function? What x values is the function concave down if #f(x) = 15x^(2/3) + 5x#? How do you know concavity inflection points, and local min/max for #f(x) = 2x^3 + 3x^2 - 432x#? How do you determine the concavity for #f(x) = x^4 − 32x^2 + 6#? How do you find the intervals on which the graph of #f(x)=5sqrtx-1# is concave up or is concave... How do you determine where the given function #f(x) = (x+3)^(2/3) - 6# is concave up and where... How do you determine the intervals on which function is concave up/down & find points of... On what intervals the following equation is concave up, concave down and where it's inflection... See all questions in Analyzing Concavity of a Function Impact of this question 1146 views around the world You can reuse this answer Creative Commons License