AP Calculus BC - Unit 1

d/dx(sinx)

cosx

d/dx(cosx)

-sinx

d/dx(tanx)

sec²x

d/dx(cotx)

-csc²x

d/dx(secx)

secxtanx

d/dx(cscx)

-cscxcotx

d/dx(lnx)

1/x

d/dx(e^x)

e^x

d/dx(a^x)

lna(a^x)

local max

x-value where f(x) is larger than all nearby outputs

f’x changes from pos to neg
f’a = o and f’’a >0

local min

x-value where f(x) is smaller than all nearby outputs

f’x changes from neg to pos

f’a = 0 and f’’a < 0

critical point

where f’a = 0 or f’a is undefined

absolute(global) max/min

x-value where f(x) is the largest/smalled for domain of f(x)

occurs at critical points or end points

point of inflection

where f(x) changes from concave up to concave down

f changes concavity at x = a

f’ changes from increasing to decreasing or vice versa

f’’ changes signs

if f’s are increasing…

f’’>0

if f’s are decreasing…

f’’’<0

if f’’ is pos…

f is concave up

if f’’ is neg…

f is concave down

for a particle to speed up…

velocity & acceleration have the same sign

for a particle to slow down…

velocity & acceleratio have different signs