What are the points of inflection, if any, of #f(x)= x^3 + 9x^2 + 15x - 25 #?

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Answer 1 · 2015-12-06T19:34:21

#(-3,-70)#

Inflection points (change in concavity) occur when the second derivative is zero.

#f'(x)=3x^2+18x+15#

#f''(x)=6x+18#

Clearly #f''(x)=0iffx=-3#

But #f(-3)=-27+27-45-25=-70#

Therefore the point #(-3,-70)# is an inflection point.

This can also be viewed from the graph of this cubic polynomial function :

graph{x^3+9x^2+15x-25 [-83.3, 83.34, -41.66, 41.63]}