Trig Derivatives Flashcards
d/dx arcsinx
1/ sqrt (1-x^2)
d/dx arccosx
-1/ sqrt (1-x^2)
d/dx arctanx
1/ (1+x^2)
Intermediate Value Theorem
if f is a real-valued continuous function on the interval [a,b] , and u is a number between f(a) and f(b) , then there is a c contained in the interval [a,b] such that f(c)=u f ( c ) = u
Mean Value Theorem
Parameters: f(x) has to be continuous and differentiable on the interval (a,b), then there is a number c such that a
Roll’s Theorem
Purpose: Prove how many roots there are
Parameters: f(x) is continuous and differentiable on the interval (a,b) and f(a)=f(b).Then there is a number c such that a
Aspects of Graphing
- Domain/Range
- X and Y intercepts
- Even or Odd function
- Asymptotes (Vertical and Horizontal)
- Increasing and Decreasing
- Minimums and Maximums
- Concavity up or down
Optimization Strategies
- Draw a diagram
- Label the variables
- Write the equations that are applicable
- Identify the domain
- Identify what is to be minimized or maximized
- Write equations in terms of 1 variable
- Find the minimum or maximum using the 1st derivative
- Plug max or min back into the original equation of one variable
d/dx (tanx)
sec^2x
d/dx (cscx)
-cscx cotx
d/dx (secx)
secx tanx
d/dx (cotx)
-csc^2x
d/dx (arccotx)
-1/(1+x^2)
d/dx (arcsecx)
1/ (|x| sqrt x^2-1)
d/dx (arccscx)
-1/ (|x| sqrt x^2-1)
