If f ' (x) > 0 on an interval then f is increasing on that 
interval.
If f ' (x) < 0 on an interval then f is decreasing on that 
interval.
Critical Numbers: 

  A number c in the domain of a function f is called a 
  critical number if either


 i) f '(c) = 0  ...
f(x) = x3 ­ x2 ­ 2x
f ' (x)
Point of inflection: 
A point on the graph where the curve changes concavity
Use nDeriv to find the local minimum of 

             f(x) = x3 ­ 4x2 + 3x ­ 5
f(x) = x3 ­ 4x2 + 3x ­ 5
Now give it a try: 

   Exercise 2.5

Questions 1 ­ 15, odd only
Derivatives Lesson  Oct 13
Derivatives Lesson  Oct 13
Derivatives Lesson  Oct 13
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Derivatives Lesson Oct 13

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Derivatives Lesson Oct 13

  1. 1. If f ' (x) > 0 on an interval then f is increasing on that  interval.
  2. 2. If f ' (x) < 0 on an interval then f is decreasing on that  interval.
  3. 3. Critical Numbers:  A number c in the domain of a function f is called a  critical number if either i) f '(c) = 0 or ii) f '(c) does not exist
  4. 4. f(x) = x3 ­ x2 ­ 2x
  5. 5. f ' (x)
  6. 6. Point of inflection:  A point on the graph where the curve changes concavity
  7. 7. Use nDeriv to find the local minimum of  f(x) = x3 ­ 4x2 + 3x ­ 5
  8. 8. f(x) = x3 ­ 4x2 + 3x ­ 5
  9. 9. Now give it a try:  Exercise 2.5 Questions 1 ­ 15, odd only
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