How do you find the intervals of increasing, decreasing and concavity for # f(x) = 2x^3 + 3x^2 - 432x #? Calculus Graphing with the Second Derivative Analyzing Concavity of a Function 1 Answer Hubert May 23, 2015 Values of #f# increase when #f'(x)>0# and decrease when #f'(x)<0#. Also #f# is concave when #f''(x)<0#. So: #f'(x)=2*3x^2+3*2x-432=6x^2+6x-432=# #=6(x^2+x-72)=6(x+9)(x-8)# #f'(x)<0 <=> x in (-9;8)# #f'(x)>0 <=> x in (-oo;-9) or x in (8;+oo)# #f''(x)=6*2x+6=12x+6=12(x+1/2)# #f''(x)<0 <=> x in (-oo;-1/2)# 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 1792 views around the world You can reuse this answer Creative Commons License