Tangent Lines and Derivatives Examples

For the function below, which is greater: f ' (0) or f ' (1)?

Draw the tangent lines to f at 0 and 1. Which has the greater slope? 

The tangent line to f at 0 is steeper than the tangent line to f at 1, so it has a greater slope. This means f ' (0) > f ' (1).

For the function shown below, which is greater: f ' (-1) or f ' (1)?

We draw the tangent lines to f at the two points in question:

Since both slopes are negative, the one that is "less negative" will be closer to zero, and so will be greater. The tangent line to f at 1 has the "less negative" slope, so f ' (1) > f ' (-1).