# 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.