So a **derivative** is like picking two points on a graph and calculating the difference in the y-values and dividing by the difference in the x-values … when the two points you pick are **infinitesimally** **close**. Up above we’ve drawn a plot of temperature *T* versus distance *x*, and we’ve shown the derivative at three points.

The way you can picture a derivative is this: If you draw a straight line that barely touches the curve at one point only, then that line is called a **tangent**. And the derivative at a point tells you the **slope of the tangent**. Where the curve is steep, the slope is high (3) and where it’s not steep slope is low (1/3). (The -ve signs are because temp goes down as x increases.)