Differentiation
Concave Upwards and Concave Downwards Curves
● Relates to the second derivative
● Concave Upwards:
d2 y
○ dx2 > 0 → gradient magnitude is increasing (either more positive or
more negative)
dy d2 y
○ dx > 0 and dx2 > 0
dy d2 y
○ dx < 0 and dx2 > 0
● Concave Downwards:
d2 y
○ dx2 < 0 → gradient is decreasing (either less positive or less
negative)
dy d2 y
○ dx > 0 and dx2 < 0
dy d2 y
○ dx < 0 and dx2 < 0
Concave Upwards and Concave Downwards Curves
● Relates to the second derivative
● Concave Upwards:
d2 y
○ dx2 > 0 → gradient magnitude is increasing (either more positive or
more negative)
dy d2 y
○ dx > 0 and dx2 > 0
dy d2 y
○ dx < 0 and dx2 > 0
● Concave Downwards:
d2 y
○ dx2 < 0 → gradient is decreasing (either less positive or less
negative)
dy d2 y
○ dx > 0 and dx2 < 0
dy d2 y
○ dx < 0 and dx2 < 0
