Presentation on theme: "Miscellaneous Topics Calculus Drill!! Developed by Susan Cantey at Walnut Hills H.S. 2006."— Presentation transcript:
Miscellaneous Topics Calculus Drill!! Developed by Susan Cantey at Walnut Hills H.S. 2006
Miscellaneous Topics Im going to ask you about various unrelated but important calculus topics. When you think you know the answer, (or if you give up ) click to get to the next slide to see if you were correct.
How many different methods are there for evaluating limits? Can you name several?
1. Inspection 2. Observe graph 3. Create a table of values 4. Re-write algebraically 5. Use LHopitals Rule (only if the form is indeterminate) 6. Squeeze theorem (rarely used!!)
If f(x) is continuous and p is a y-value between f(a) and f(b), then there is at least one x-value between a and b such that f(c) = p.
What is the formula for the slope of the secant line through (a,f(a)) and (b,f(b)) and what does it represent?
average rate of change in f(x) from x=a to x=b Note: This differs from the derivative which gives exact instantaneous rate of change values at single x-value but you can use it to the derivative value at some values of x=c between a and b.
FIRST DERIVATIVE TEST If f (x) changes from + to – at x=a then f(a) is a local maximum. If f (x) changes from – to + at x=a then f(a) is a local minimum. Dam thats a good test!! Dam, thats a great test!!