# First Derivative Test

## First Derivative Test

by Theresa Guard
## 1. find the derivative

### 1.1. power rule

### 1.2. product rule

### 1.3. quotient rule

## 2. set the derivative equal to zero and solve

### 2.1. factor

### 2.2. quadratic formula

### 2.3. graphing

### 2.4. synthetic division

## 3. make a chart

### 3.1. break the domain into intervals using the zeros of the derivative

### 3.2. chose a test point in each interval

### 3.3. plug the test point into the derivative to determine if it is positive or negative

### 3.4. If the derivative is negative, the function is decreasing and If the derivative is positive, the function is increasing

## 4. Determine Maximums or Minimums

### 4.1. If the function changes from increasing to decreasing, there is a maximum

### 4.2. If the function changes from decreasing to increasing, there is a minimum

### 4.3. Plug the x value into the original function to find the value of the maximum or minimum.

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