Definition of the derivative of a polynomial function
This slide continues the ideas in the previous one. We see that the (t,x) graph is complicated. If we draw tangent lines to it at various places to produce a (t,v) graph, the plotted points vary wildly both above and below the axis. It would be good if there was a rule to plot a function that would give us the slope of the original function at any time t- in other words, given the original position function, being able to generate a velocity function. Fortunately, for polynomials, there is a very simple such rule, which is in light green at the extreme right of the screen. A parabola, the most common position function we'll use in this class, is shown with the rule for taking the derivative of a polynomial. y=t^2 becomes v=2t. Some polynomial practice is shown at the bottom of the screen.
Definition of the derivative of a polynomial function
This slide continues the ideas in the previous one. We see that the (t,x) graph is complicated. If we draw tangent lines to it at various places to produce a (t,v) graph, the plotted points vary wildly both above and below the axis. It would be good if there was a rule to plot a function that would give us the slope of the original function at any time t- in other words, given the original position function, being able to generate a velocity function. Fortunately, for polynomials, there is a very simple such rule, which is in light green at the extreme right of the screen. A parabola, the most common position function we'll use in this class, is shown with the rule for taking the derivative of a polynomial. y=t^2 becomes v=2t. Some polynomial practice is shown at the bottom of the screen.