What are the points of inflection, if any, of #f(x)=-3x^3+270x^2-3600x+18000 #?

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Answer 1 · 2016-10-28T02:35:26

At #x=30#, there is a point of inflection

Given -

#y=-3x^3+270x^2-3600x+18000#

To find the point of inflection we have to set the send derivative equal to zero.

#dy/dx=9x^2+540x-3600#

#(d^2y)/(dx^2)=18x+540#

Set #(d^2y)/(dx^2)=0#

Then -

#18x+540=0#
#x=540/18=30#

At #x=30#, there is a point of inflection