What is the significance of taking a derivative when you have to have the information to plot a graph accurately to begin with?
- L. E. GantLv 76 months ago
The derivative is the slope of the tangent to the curve. It's a useful tool to find what are called maxima, minima and "turning points" on the curve (the points at which the curve has tangents that are parallel to the x-axis.
Usually, your graph is based on a function, rather than a series of points. Most functions that are used are continuous and differentiable, and not have singularities (or holes)
- Mike GLv 76 months ago
Speed - you can instantly get the turning points without plotting the whole graph. Also, where the function is increasing or decreasing.