# What are the points of inflection, if any, of #f(x)=x^7/42 - (3x^6)/10 + (6x^5)/5 - (4x^4)/3 #?

##### 1 Answer

The only inflection point is

#### Explanation:

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:

But

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