How many inflection points are in the graph of #f(x)= (x^7)/42 - (3x^6)/10 + (6x^5)/5 - (4x^4)/3#?
There is one inflection point.
Finding the zeros of
# = x^2(x^3-9x^2+24x-16)#
Rational Zeros Theorem and checking (or inspection of likely candidates or adding the coefficients) we see that
Factor or do the division to get:
# = x^2(x-1)(x-4)^2#
The zeros are
The sign of
Therefore the only inflection point is