What are the points of inflection, if any, of #f(x) = 4x^6 +4x^5 -5x^4 #?

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Answer 1 · 2016-04-23T20:54:54

#x=-1.155, .448#

Let's find the second derivative...

#f'(x)=24x^5+20x^4-20x^3#

#f''(x)=120x^4+80x^3-60x^2#

There it is, the second derivative. How about we set the second derivative equal to zero...

#f''(x)=120x^4+80x^3-60x^2=0#

#20x^2(6x^2+4x-3)=0#

#x=-1.155, 0, .448#

Do some analysis of these points, just to make sure. You'll be glad you did that, for your answers are...

#x=-1.155, .448#