What are the points of inflection, if any, of #f(x)=x^7/42 - (3x^6)/10 + (6x^5)/5 - (4x^4)/3 #?
The only inflection point is
In order to determine where the concavity does change, we must first determine where it might change.
Use inspection or the rational zeros test to see that
Then use division or trial and error to factor
# = (x-1)(x-4)^2#
This gives us:
The sign of
( Note: this could also be determined by using a sign chart for
The inflection pint is the point
The inflection point is