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Derivatives (Laws (f'(sec x)=(tan x)(sec x), f'(csc) = (-cot…

- - - - Follows chain rule, but set g(x)=u
- - - - Removable Denominators are removable points
      - Non-removable denominators cannot = 0, creates vertical asymptote
      - sqrt() cannot have negative numbers
      - |x| can never be less than 0
      - HA are when x/x = a/a, x^2/x=none, x/x^2=0
    - - tan(90) = undefined
      - cot(90) = undefined
      - sin(0)=0
      - cos(0)=1
      - cos(90)=0
      - sin(90)=1
  - - - same = even, same*-1= odd, different=neither,
    - - Plug in -x and find if function is same
    - - Plug in -y and find if function is same
    - - y and x-axis symmetry are true
- - - - If f(x) is continuous from [a,b] then the local max and min are within that interval
    - - If f(x) is continuous from [a,b] and is differentiable from (a,b) then
        f'(c) = [f(b)-f(a)]/(b-a)
    - - I f(x) is continuous from [a,b], c is a limit in that interval
  - - - Use a number line to identify the domain interval
    - - Theorem 3.5
        
        f'(x) > 0, f(x) is increasing
        
        f'(x) < 0, f(x) is decreasing
        
        f'(x) = 0, f(x) has a slope of 0
- - - - Take derivative of equation.
      - Create an equation
      - Plug in to find dy/dt
      - Find unknowns of dx/dt, and x