Local straightness
The rate of change of a variable whose graph is a straight line is just the gradient (or slope) of the straight line graph. For a curved graph, this approach seems to fail because the gradient of the graph varies along its length. However, if we look at a small part of the graph which magnifies to look (reasonably) straight, then we can see the gradient of the graph. It is the gradient of the (nearly) straight magnified part of the graph. A graph is said to be locally straight if it magnifies to ‘look straight’everywhere along its length. We can can therefore look along such a curve and see its gradient changing. This gradient function, calculated symbolically in a perfect way, is the derivative of the function. The study of the conversion of locally straight visual images into symbolic calculus of the derivative is called a locally straight approach to calculus. 
