What are the points of inflection, if any, of #f(x) = 2x^3 + 3x^2 - 432x #?

1 Answer
Oct 5, 2016

At inflexion points, the curve changes its concavity. We can test for these changes using the 2nd derivative, for when #f''(x)=0#. Keep in mind that this does not work for all functions (an example would be for #x^4#). Use a sign table/table of values to check if you are unsure (to see if the point is a turning point or an inflexion point).
#f'(x)=6x^2 + 6x -432#
#f''(x)=12x+6#
Solving for #f''(x)=0#
#12x+6=0#
#2x=-1#
#x=-1/2#
At #x=-1/2, f(x)=433/2#
So the point of inflexion is at #(-1/2,433/2)#