What are the points of inflection of #f(x)= x^3 + 5x^2 + 4x - 3#?

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Answer 1 · 2016-10-25T14:00:13

There is only one point of inflection at #(-1.667,-0.407)#

To determine points of inflexion, we look when #f''(x)=0#

#f(x)=x^3+5x^2+4x-3#

#f'(x)=3x^2+10x+4#

#f''(x)=6x+10#

#f''(x)=0 =>6x+10=0#
#x=-10/3/6=-5/3=-1.667#

#f(-5/3)=(-1.667)^3+5(-1.667)^2+4(-1.667)-3=-0.407#

graph{x^3+5x^2+4x-3 [-10.915, 9.08, -5.74, 4.26]}