Took assessment. That's it!
Homework
none :)
Tuesday
Went over assessment in detail, then worked on AP Derivatives Rules packet.
Homework
this packet, due Monday (link)
Wednesday DS
Learned about finding horizontal and vertical tangents. Basically you take the derivative, simplify it (often yielding a fraction through clever factoring) and then set the numerator =0 and solve to find horizontal tangents and set the denominator =0 to find vertical tangents.
Notes from board
video similar to lesson
Learned about linear approximation and normal lines. Because differentiable functions are 'locally linear', the tangent line is a good approximation for the function it is tangent to, near the point of tangency. Thus we can use it to estimate values that are difficult to plug into the curvy function. Basically you do all the same work for finding the tangent line (using a known input/output pair for the function being estimated) and then you plug the challenging/weird/exotic number into the tangent line for X and solve for Y. The Y is the estimate.
We also learned about normal lines. Normal is a synonym for perpendicular. You do all the same work for finding a tangent line, except your M isn't the value of the derivative at the X-value, but rather the opposite reciprocal of the derivative's value. This is because perpendicular lines have opposite reciprocal slopes (think back to Algebra I and Geometry). Then we played the tangent line game, which we will finish on Monday.
Notes from board
Homework
this packet, extended due date to Tuesday (link)
Resources
tangent line approximations: link