chapter 3

Question 1

How would you calculate a derivative involving e?

Answer 1

calculator, you dont know what e is but you can treat it like a variable for some reason

Question 2

must points of inflection always be differentiable?

Answer 2

no, in fact points of inflection can ONLY exist as a zero or an undefined value (f”(x) = 0 or x/0)

Question 3

What are the 3 cases for horizontal asymptotes?

Answer 3

numerator >denominator degree: none

equal: whatever coefficient is next to the highest power variable

numerator lower degree than denominator: y = 0

Question 4

https://www.youtube.com/watch?v=V5_sUs-hJPg

Question 5

true/false: any constant over any variable in an infinite limit question = 0

Answer 5

true

Question 6

when is a number critical?

Answer 6

when the prime of that function relative to a given critical # is undefined or 0

Question 7

I/D test

Answer 7

creating a sign chart and determining intervals of icnrease/decrease

Question 8

first derivative test

Answer 8

using the I/D test, if f’(c) goes from negative to positive = min, from positive to negative = max

Question 9

second derivative test

Answer 9

if f’(c) = 0 (min/max as determined by first derivative test) and f”(c) = positive, then minimum, and if negative, then maximum (CU vs CD)