derivates memory test 2 Flashcards
if derivate exists at a point
- not discontinuous
- smooth graph
- no corner
- no cusp
- no vertical tangent
average rate of change on [a,b]
b-a
definition of derivative
h
notation for instantaneous rate of change (derivative at a point):
d
— [f(x)]
dx
derivatives of constant & linear functions
d
— [c] =0 or c
dx
sin x
cos x
cos x
- sin x
tan x
sec ^2 x
cot
- csc ^2 x
sec x
sec x tan x
csc x
- csc x cot x
e^ x
e^ x
ln x
x
ln (x+d)
x+d
writing tangent line
slope = f’(a)
point f(a)
y-f(a)=f’(a)(x-a)
writing normal line
point: f(a)
slope: -1
—-
f’(a)
y-f(a)=-1
—- (x-a)
f’(a)
finding linear approximation
write tangent line
plug in x-value to approximation and find y
justifications for linear approximation estimates
a linear approximation (tangent line) is an overestimate if the curve is concave down
a linear approximation (tangent line) is an underestimate if the curve is concave up
justification for horizontal tangent lines
dy
—- = 0
dx
justification for vertical tangent lines
dy
—- = undefined
dx
sin ^-1 x
square rt 1-x^2
cos ^-1 x
- ## 1square rt 1-(kx)^2
