# If #y = 3x^5 - 5x^3#, what are the points of inflection of the graph f (x)?

##### 2 Answers

#### Explanation:

At a critical point

So there are three critical points, when

To determine the nature of these critical points we look at the second derivative:

So When:

So the nature of the critical points is as follows

The points of inflection (with rationalized denominators) are:

#### Explanation:

Points of inflection are points on the graph at which the concavity (and the sign of the second derivative) change.

The zeros of

The solutions are

Each of these is a zero of the polynomial

Therefore each is the

The points of inflection (with rationalized denominators) are: