Showed how to find variables to make a function differentiable. First make it continuous, creating a two-variable equation. Next, take the derivative of the given function (usually piecewise) and make this new derivative function continuous. Solve the remaining system of the equations.
Then look at units and how position can be measured in meters, velocity in meters per second (m/s) and acceleration in meters per second per second (or m/s^2). This fits nicely with the concept we saw of a given position function's first derivative being velocity and its second derivative being acceleration (or the change OF the velocity). To find a higher order derivative, simply take the derivative of a derivative using the same rules and procedures as before.
Lecture notes
Homework:
selected worksheet problems (see last post) due on Wednesday
Assessment on trig derivatives, chain rule, and review on Wednesday
Resources:
make a function differentiable (sorry for shaky video) https://www.youtube.com/watch?v=eWK1GjoyQXg
how to find a second derivative: https://www.youtube.com/watch?v=3aVT9d_RTsk
derivatives/differentiability of piecewise functions: https://www.youtube.com/watch?v=Ei9p_h0mL_w
great position/velocity/acceleration examples: https://www.youtube.com/watch?v=UxYwLcZwJCs
Wednesday
(sub was present) Went over homework on trig derivatives and chain rule. SOLUTIONS HERE. Took assessment on these skills and some review. Then wrote equations of normal and tangent lines in more complicated problems. Some example problems from Thursday DS linked here
Homework: Worksheet
due Weds of next week (D-CD7)
Resources:
normal line example: https://www.youtube.com/watch?v=pxE2PNxu_8k
Clicker activity to review assessment concepts. Here are the problems for you to review. Also here is #9 from the assessment worked out: https://www.youtube.com/watch?v=YOGLKbxE5QQ
Then we used computers and the applets linked below to explore derivatives from a graphical perspective.
Here is the worksheet that goes with the website below.
LINK TO APPLETS: http://webspace.ship.edu/msrenault/GeoGebraCalculus/GeoGebraCalculusApplets.html
Homework: finish online derivatives: graphical exploration worksheet for Monday
tangent and normal line worksheet due Wednesday (D-CD7)
Resources
some tangent and normal line worksheet problems worked out to help you linked HERE