First Derivative Test Introduction and Examples by mes

hive-128780 · @mes · Jan 27 '23 (edited)

$3.95

First Derivative Test Introduction and Examples

https://youtu.be/60UMYG7Ppeg

In this video I introduce what the first derivative test is and how you can use it to graph a function by first determining when the function is increasing or decreasing and thus where it has its local max or minimums.

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# First Derivative Test Introduction and Examples

![First Derivative Test 1080p.jpeg](https://files.peakd.com/file/peakd-hive/mes/23wCdHrzXL5JS6hdjeJvFngD4yjdMMQutd21ntRLMq6diSt2BbUuwdPHXoDjLMANdWkux.jpeg)

## How the derivative affects the shape of a graph

![image.png](https://files.peakd.com/file/peakd-hive/mes/Eo4Js77WstipXAnXx9RqwjPtMuviCCJm1nztoJ5fnM77sUeMthoCQYPfwfLkBCMcA3L.png)

## Increasing / Decreasing Test

![image.png](https://files.peakd.com/file/peakd-hive/mes/23sxpRyy9Khwjz3BhmzLY6AWhqtRaGWr571YeSJkA24KvhnXHPyHe5uSLA6F2cakQtHme.png)

# First Derivative Test

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8D1dSg517dBTW7JXvKSbGN6xvEBfbr43Pux2ybPbwbmC626U8DrTgZM74hjyBE2kzy.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23sxpXQpjbDE1JugJpyoR8q8iT3mm3YqtCUxnmGj65cF8X7a7RMyyzWZ2J8kbtDRYKMi9.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/Enz43VKAAnVd2hGF97Dxv3vA6wJ6jymGn3sA7Mm1Y9hkYh47toU1gLCGpjsMcFAemAg.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tSzWXZGprCFw8SBV2JYb6yrVt93qJnL6Mak82xmf4CWsPm8W4FEj28BDdwoAWse8dk2.png)

# Example 1

![image.png](https://files.peakd.com/file/peakd-hive/mes/23uFweEVGMRALLhdq26JN814Tnf7UeJt6fYwbPhzj25AbxfKuqFjSqmS3PvhaAQcKmSsy.png)

**Solution:**

![image.png](https://files.peakd.com/file/peakd-hive/mes/23sxozwpRCkaLzDai2S3uLRK5BBxAL7NjjCus23xA2d8cB75xzPhW83rGRAoWh765bq6f.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8DBnQEtNLPF6dLDS1oZDjq41dzJ3UMrXMajbEaRrG83S9GhXwKXcRF1ZdEJrBDv6Zu.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8DBnQF2rBvRVKsK84oMkAKBaNU4LWHprTd99iHkH4vCSBXn3CGbPvDm3Z8gRamziCm.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9yksdJ3wqMZvqFHiF88diJCioejgbZZ781Pi9CmbTVgs6AbPNQ2cAQLkmB9zzXy.png)

# Example 2

![image.png](https://files.peakd.com/file/peakd-hive/mes/Enz3vqbteNmKyKW3fTh7btnwUxRkSm8w822xEhQxWcixQgJGH46yeFwArHYfMRDmZcd.png)

**Solution:**

![image.png](https://files.peakd.com/file/peakd-hive/mes/23sxozwpQmJqt62VrggEDKehDg6yEHzzHfT3xMgHAGvrkDEA7Jj56TUsBCW57M6FGtYqJ.png)

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