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when f(x) is increasing
f’(x) is positive
when f(x) is concave up
f’(x) is increasing and f’’(x) is positive
when f(x) is decreasing
f’(x) is negative
when f(x) is concave down
f’(x) is decreasing and f’’(x) is negative
when f(x) has a inflection point
f’(x) has a local min/max and f’’(x) has a zero
when f(x) has a vertical tangent
f’(x) is undefined
if f(x) has a sharp corner or cusp
f’(x) is undefined
when f(x) is discontinuous
f’(x) is undefined
where f(x) has local min/max
f’(x) is 0
where f(x) has an inflection point
f’(x) has a local max/min
inflection point
when the graph changes direction
acceleration
f’’
velocity
f’
position
f
f’(sin x) =
cos x
f’(cos x) =
-sin x
f’(sec x) =
sec x tan x
quotient rule
f'(x)g(x)-g'(x)f(x)/g(x)2
product rule
f’(x)g(x)+f(x)g’(x)
In e
1
d/dx e^x
e^x
exponential function
d/dx a^x = ln (a)(a^x)
f(x) has a maximum
f’(x) switches from positive to negative at a 0
f(x) has a minimum
f’(x) has a 0 and changes from negative to positive
Note 
Flashcard (46)