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HOW TO FIND THE MINIMUM OF A FUNCTION WITH TI89 CALCULATOR

Steps Key Sequence Screens
1. Input Function or Piecewise-Defined Function. Press DIAMOND key, then F1 key (for Y=)
  Type the function
Method 1: Using home screen. This method finds the largest local minimum (not necessarily a global minimum!).
2. Go to Home screen Press 2nd, then ESC
3. Select fMin function Press F3
  Press 6 (for fMin()
4. Type in Function  
Note: You can either type in the function directly (e.g., 5 – 2x2 + x3) OR, if you followed step 1 above, use y1(x)
4. Type in Independent Variable Press comma key, then x, then right parenthesis
Note: This will find the minimum of the function on the whole domain of the function. If this is the value for which you are looking, then goto Step 8. If you want to limit the domain of the function to a specific closed interval then goto the next step.
5. Type in First Restriction (i.e., left endpoint) Press | key
  Type X key
  Press 2nd, then 5 (for MATH menu)
  Press 8 (for Test submenu)
  Press 3 (for >=)
  Type in value for endpoint
6. Type in and function Press CATALOG key
Note: You will need to scroll using up or down arrow keys to find 'and'. To quickly move to the 'a' functions, press = key.
  ENTER (to select 'and')
7. Type in Second Restriction (i.e., right endpoint) Type X key
  Press 2nd, then 5 (for MATH menu)
  Press 8 (for Test submenu)
  Press 4 (for <=)
  Type in value for endpoint
8. Solve ENTER
Note: If this returns an equation, then press DIAMOND key, then ENTER!
 
Method 2: Using grapher.
Follow Step 1 above    
  Type the function
2. Graph Press DIAMOND key, then F3 key
3. Find Minimum Point Press F5
  Press 3 (for Minimum)
  Type in x-value for a point to the left of a suspected local minimum point or trace function until you reach the value for x
Note: The minimum point will be the smallest y-value in the interval between the lower bound and upper bound.
  Press ENTER
  Type in x-value for a point to the right of a suspected local minimum point or trace function until you reach the value for x
  Press ENTER
Note: In this case, the minimum of the function on [0, 3] is 3.81481 and occurs at x = 1.33333.