1. Fun facts
about derivatives

2. Daffy-nition

3. Daffy-nition
is a mathematical operation on the function f(x). The operator is the symbol

4. Derivative of a constant
f (x) = constant, f ' (x) = 0

5. Constant multiplier
f'(ax) = a f'(x)

6. Power rule

7. Meaning of the derivative
slope of tangent line

8. When the derivative is positive,
the function is increasing

9. When the derivative is negative,
the function is decreasing

10. the function has a horizontal tangent
When the derivative is 0
the function has a horizontal tangent

11. the function may have a max or a min, but...
When the derivative is 0
the function may have a max or a min, but...

12. When the derivative is undefined
the function might also have a min or a max

13. Values of x where the derivative is either 0 or does not exist
are called CRITICAL POINTS of the function

14. You must remember to check the function at ALL critical points
to find the function's mins and maxes

15. The product rule
(fg) ' = f 'g + g'f

16. The quotient rule
“lo dhi – hi dlo over lo lo”

17. is the derivative of the derivative
The second derivative
is the derivative of the derivative

18. The second derivative

19. The End
…for now…