1. First and Second Derivative
f ’(x) = 0 Horizontal
f “ (x) > 0 Positive Concave up Ball is Collected
f “ (x) < 0 Negative Concave down Ball is falling
f ’(x) = 0 Horizontal
f “ (x) > 0 Concave up
f “ (x) > 0
Concave up
f “ (x) < 0 Concave down
f “ (x) = 0 Ball is Switching
f “ (x) = 0 Ball is Switching
f “ (x) < 0 Concave down

2. _ _ + + Easy Way to Remember The Second Derivative
f “ (x) > 0 , Concave up
Happy Minor
f “ (x) < 0 , Concave down
Mad Max

3. First and Second Derivative
f ’(x) > 0 Positive Rising, Increasing
f “ (x) > 0 Positive Concave up
f ’(x) > 0 Positive Rising, Increasing
f “ (x) < 0 Negative Concave down
f ’(x) < 0 Negative Falling, Decreasing
f ’(x) < 0 Negative Falling, Decreasing
f “ (x) < 0 Negative Concave down
f “ (x) > 0 Positive Concave up