Because the slopes of the points of a function have numerical values, these numbers can be plotted to create both another graph and another function. The derivative function is the derivative of a y value at an x value. Because the derivative is the instantaneous change which merely looks at the average rate of change for 2 points infinitely close, the f' can also be written as change in y over the change in x. The equation for this is delta y is approximately f' times delta x.
Challenges.
How can a a bunch of tangent lines (the derivative) form a graph? Why can f'=delta y/delta x. F' is the slope of the tangent line, not f(x). Why does the derivative show how quickly the function is chaning?
Reflections
When first reading the section about derivatives having derivatives, it made no sense to me. I just remembered though that in calc last year we found f' and f'' and f'''. It makes sense because you can graph velocity and acceleration and jerk.
No comments:
Post a Comment