How to Graph a Function

How to Graph a Function

1. 4) Identify absolute extremas (max/min)

   • First, use the critical points found to aply the first derivative test.
   • Finally, Graph, and locate absolute extremas by plugging x-values to get the y-values.

2. 5) Identify inflection points

   • First, if the graph is below the tangent line it is concave down.
   • Second, If the graph is above tangent line is concave up.
   • Finally, a change in concavity is equal to an inflection point

3. 1) Find Critical Points

   • Second, equal the function to zero and solve.
   • First, derive the function.
   • Finally, the points found are the critical points.

4. 2) Determine which intervals are increasing and decreasing

   • First, use the critical points to subdivide the domain.
   • Finally, look for the final sign (+ or -) to determine if its increasing or decreasing

5. 3) Determine local maximum and minimum

   • First, you need to have your increasing/decreasing intervals, and the x value is the local max/min.
   • Second, if the x value goes from - to + x will be the local minimum.
   • Finally, if the x value goes from - to + x will be the local minimum.

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