calculus Flashcards
increasing at an increasing rate
decreasing at an increasing rate
increasing at a decreasing rate
decreasing at a decreasing rate
check concavity within?
placing x values within the d2y/dx2 function (MAKE SURE YOU WRITE CONCAVITY)
when is f(x) increasing?
when f’(x)>0
when is f(x) decreasing
when f’(x)<0
point of inflection when?
f”(x) = 0 - check for concavity
point of inflection when (graphs)
when f’(x) has a turning point
differentiation of sinx
cosx
d/dx of cosx
-sinx
d/dx of sinx°
use this for all trig functions
π/180 cosx°
as x° = π/180x
d/dx of arctanx
1/1+x^2
d/dx
f’(x)/ln(a)*f(x)
or you can do the base of e rule
you can do the base of e rule
how to differentiate abs (x-3)
split it into the 3 arms
now you are able to differentiate each arm
what happens to the derivative if the function is discontinuous
can have a vertical tangent at the discontinuity when the sign is the same, on either side of the discontinuity
dy/dx = 1/3x^-2/3
what happens to the derivative when the function is dicontinuous
can have a cusp = only when the sign on either side are opposite
how to calculate abs/global max/min
max sure you test the boundaries and also test the derivative for any max/min TP
