ap calculus theorems/ rules

intermediate value theorem

if f(x) is continious from [a,b], then it’s continious every y value between f(a) and f(b) at least once

what’s a limit?

when a value APPROACHES something

derivative; how many pts

is an instanteneous rate of change of a tangent line

average rate of change

• (f(b)-f(a))/(b-a)

• secant line

• estimate values example if ur trying to find 1 and only the points 0 and 2 are given then u would use this formula

which formula returns a f’(x)?

lim f(x+h)-f(x)/h

x→h

which two formulas returns a derivative at a point?

lim f(x+x)-f(c )/h

h→0

lim f(x)-f( c)/ x-c

x→ c

tanx derivatiive

sec²x

d sexc

secxtanx

d cscx

-cscxcotx

d cotx

-csc²x

d e^x

e^x

d lnx

1/x

normal line

perpendicular to the derivative

tangent line

j find the derivative and plug the x-value

inverse formula

f’^-1(a)= 1/f’(b)

finding speed

postive it’s the absolute value of v(x)

mean value theorem

if f(x) is continious on a closed interval, if f(x) is differentiable on an open interval that means c exists.

second derivative test

if f’’(x)>0 theres a concave up and there’s a min, if it’s <0 there’s a concave down and there’s a max