What are the points of inflection, if any, of #f(x) = -3x^4-2 x^3 +9 #?

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Answer 1 · 2016-01-03T15:42:04

In order to find the points of inflection we need to find the roots of

#f''(x)# eg the second derivative of the function.

Hence from

#f''(x)=0=>-36x^2-12x=0=>12x*(3x+1)=0#

so the roots are

#x=0# and #x=-1/3#

The possible points of inflection are #x=0# and #x=-1/3# .

But Inflection points are where the function changes concavity.This is happening only for #x=0#

So the inflection point is #(0,f(0))# or #(0,9)#