Given+the+graph+of+f+′(x),+sketch+a+possible+graph+of+f(x)

While no definate range values can be obtained, looking at the graph of a derivative can allow one to sketch the crude image of a graph by following five simple rules.

1. The domain interval where the graph of the derivative is evaluated to have a positive range the original graph is increasing.

2. The domain interval where the graph of the derivative is evaluated to have a negative range the original graph is decreasing.

3. The domain point or interval where the graph of the derivative is evaluated to have a value of zero the original graph is neither increasing or decreasing but reaining constant as horizontal.

4. The domain point or interval where the graph of the derivative cannot evaluated is either a cusp, corner, or discontinuity if a point, or an undefined section of the graph if an interval.

5. If the limit at an undefined point equals either positive infinity or negative infinity then the original graph is vertical at that point.