# How do you sketch the curve #y=x^3-3x^2-9x+5# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?

##### 1 Answer

graph{x^3-3x^2-9x+5 [-145.9, 172.6, -85.6, 73.6]} FIrst determine the interval of definition, then the behavior of first and second derivatives and the behavior of the function as

#### Explanation:

1) The function is a polynomial and is defined for

2) The highest monomial is of odd order so:

Also

3) Calculate the first and second derivative:

The points where

In both points the second derivative is non null, so these are local extrema and not inflection points.

If we analyze the sign of

So,

4) Analyze the value of the function in the local extrema:

So there will be three real roots: one in