First Derivative Test

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.