Second Derivative Test Example - Sketching y = x^4 - 4*x^3

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Second Derivative Test Example - Sketching y = x^4 - 4*x^3
https://youtu.be/_Ew7ZpBJxPw

In this video I illustrate further on using the Second Derivative Test by going over a very useful example to show how you can use this test to help sketch a function by hand, noting where it is concave upwards or downwards, local max and min, and the inflection points.

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# Second Derivative Test - Examples

![Second Derivative Test - Examples 1080p.jpeg](https://files.peakd.com/file/peakd-hive/mes/23z7dVhY2fXFNzPvoBFRbU7L93VuoaufhNpeh4bBhFvWEyTaZvxxpwxNBEyHqhZBytvmK.jpeg)

## Recap on Second Derivative Test

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8DBnQF2rAS8senggXyKSEKyCNsewUif9a4TvCeCpPkQPpbtPjQXkGELJwX8YoDcvaC.png)

# Example

Sketch the curve **y = x<sup>4</sup> - 4x<sup>3</sup>** and determine concavity, inflection points, and local max / min.

## Solution

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8DBnQFL2UYUnBnCEk2sxLTQZApXuQzX4ygwCJSZ1yuLmqETDJPuj6wL2udQ7aDHqW5.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbKgySYywth7EZLDUYxZD7vX6teTV59RAaBqPAYgx6wjCwC55WBmivQBCqN4MDPsnF.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9ykrH5XwPQZwArWnfappbPMHuACtGGmrtSZrLjgQMLn9hfNw8TZVvUx6dj5nUV8.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9ykh98b5pnpLDNJqjLFQGyhxZYpPTG24shoUvupDqzXeU6zQUGeySFRYgQysJvF.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8CfKPvxwpaCX475AKRgBrP8ZTSZMdTgkatrthGicfYCJYnVmKUp3sbwc8E73rqpBaD.png)
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