Calc 1 - Unit 3.3-3.5

First derivate vs Second derivative

First derivative - tells you inc/dec, and relative extrema

Second Derivative - tells you concave up/down, POI

What do the 1st/2nd Derivative tests find

Relative Minimums and Maximums

How to do 1st Derivative Test

1. Find critical #’s from 1st derivative

2. Put the #’s in a chart

3. Where sign changes is where there is a Rel. Min/Max

4. + to - is relative max; - to + is relative min

How to do 2nd Derivative Test

1. Find critical #’s from 1st derivative

2. Find 2nd derivative and plug critical #’s to test if +/- y-value

3. If positive y-value it is relative min; negative y-value it is rel. max

4. Plug Critical #’s back in original function to find other point

Why would 2nd derivative test be better than first

If you’re dealing with straight polynomials with easy to find derivatives

How to tell when you can’t use 2nd derivative test and have to go back to first

If when plugging critical #’s into derivative, you get 0 and not a positive or negative value

Where do you find POI?

2nd derivative chart; where there’s a sign change

Where do you find relative min/max?

1st derivative chart; where there’s a sign change

Where do you find increasing/decreasing intervals

1st derivative chart

increasing where positive, decreasing where negative

Where do you find ujp/down concavity

2nd derivative chart

concave up where positive, down where negative

When doing infinite limits and hor. asymptotes, when do you have to divide everything by the highest denominator power? (Not the shortcut method)

when you get “0/0” or “∞/∞” or when you don’t have a rational function

Which type of functions approach the same hor. asymptote from both sides

Rational Functions; Straight Polynomials; no Square root, etc.

Rational Function 3 Rules Shortcut:

1. degree in num > denominator = ±∞ (depends)

2. degree in num < denominator = 0

3. degree in num = denominator = ratio of leading #’s