What are the points of inflection of #f(x)=x^3-3x^2-x+7 #?

1 Answer
Jan 16, 2018

At #x=1#

Explanation:

The point of inflection is the point where the second derivative of the function #f(x)# is zero i.e. #(d^2f)/(dx^2)=0#. At these points the slope of the curve changes from increasing to decreasing and vice versa.

Here function is #f(x)=x^3-3x^2-x+7#

and #(df)/(dx)=3x^2-6x-1# and #(d^2f)/(dx^2)=6x-6#

and #(d^2f)/(dx^2)# is zero, when #6x-6-0# or #x=1#

and at this #y=4#

graph{(x^3-3x^2-x+7-y)((x-1)^2+(y-4)^2-0.01)=0 [-5.043, 4.957, 1.54, 6.54]}