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

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

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