1
Q
critical value (cv) on f(x)
A
f’(x)=0, undefined, or DNE
2
Q
point of inflection (POI) on f(x)
A
f’(x) changes behavior (inc/dec)
f”(x) changes sign (+/-)
3
Q
f(x) increasing
A
f’(x)>0 (+)
4
Q
f(x) decreasing
A
f’(x)<0 (-)
5
Q
local maximum on f(x)
A
f’(x)=0 and changes from (+) to (-)
f’(x)=0 and f”(x)<0 (-)
6
Q
local minimum on f(x)
A
f’(x)=0 and changes from (-) to (+)
f’(x)=0 and f”(x)>0 (+)
7
Q
f(x) is speeding up
A
f’(x) and f”(x) are the same sign
8
Q
f(x) is slowing down
A
f’(x) and f”(x) are opposite signs
9
Q
f(x) is concave up
A
f’(x) is increasing
f”(x)>0 (+)
10
Q
f(x) is concave down
A
f’(x) is decreasing
f”(x)<0 (-)
