Went over IVT homework. Solutions are included in the notes below to help you study, but as always work is expected on hw to allow for a retake. Put the limit definition of derivative into our foldable books, then applied it to a quadratic equation to find its derivative and the slope of its tangent line at a specific point.
Notes from board
Homework
- p103 #11-18 [D-C1]
- Assessment in DS on Wednesday: What is on it?
-similar to homework reviewed today + AP IVT questions handed out Friday [F-C4] (Remember that a function must be continuous for IVT to apply. Must state that before applying)
- Showing that a function is (dis)continuous [F-C1]
- Finding and justifying discontinuities [F-C3]
Assessment Study Resources
showing that a function has a root in a given interval: link
finding the value of c guaranteed by the IVT: link
checking to see if a function is continuous or not: link
finding, classifying, and justifying discontinuities: link
Homework Resources
limit definition example to find the derivative function (note that h stands in for delta-x here): link
some more examples: link
Assessed on IVT and continuity review problems in DS. Debriefed test in class with peer experts; this test can be retaken in DS so long as hw is completed. Warm-up dealt with finding the derivative of a linear function quickly, by realizing the derivative describes a function's slope, and a linear function's slope is constant and self-evident as the "m" in "mx+b".
Introduced a real-world example of change in a financial context and how finding value (plugging a number into the function) differs from finding the rate of change (plugging a number into the derivative...which first has to be found). The modeling function was too cumbersome for the limit definition of derivative, so we did a numerical investigation into the patterns of derivatives involving power functions like x^2, x^3, x^4, and so on. Looking at numerical patterns revealed the pattern called the power rule for derivatives:
Homework:
none -_-
if you want a head start, due Monday will be p114 #3-18, 25-30, 39-46 [D-C7]
Resources
power rule simple examples: link
Warm up dealt with using the Power Rule in 3 cases, one traditional, one sneaky, and one that was evil looking but actually straight forward once you recognize the limit definition of derivative. Did another real world example problem, dealing with a falling object and calculating the velocity at a certain time by using the derivative.
Looked at some fun 'calculus cartoons' to help personify the limit definition of derivative and the power rule, along with 'cleaning a function up for prom' by rewriting it. This led to some helpful hints regarding negative exponents, nth roots, and simplifying before taking the derivative. Remainder of time was spent on homework and/or reassessing.
Notes from board
Homework
p. 114 #3-18, 25-30, 39-46 [D-C7]
use calcchat.com to help with odd numbers you're having trouble with
ABSENT FRIDAY?? Here's what you need to know for the homework;
- rewrite rational terms and nth roots as exponents: here's how to handle rational terms: link and here's how to handle a simple square root; see here for other roots.
Resources
power rule for rational functions (#25-30) link [also see p 110 ex 6 at top of page]
rewriting involving nth roots and fractions: link (starts at 3:35)