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## HOW TO FIND THE MAXIMUM 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 maximum (not necessarily a global maximum!). 2. Go to Home screen Press 2nd, then ESC 3. Select fMax function Press F3 Press 7 (for fMax() 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 maximum 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 2. Graph Press DIAMOND key, then F3 key 3. Find Maximum Point Press F5 Press 4 (for Maximum) Type in x-value for a point to the left of a suspected local maximum point or trace function until you reach the value for x IMPORTANT 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 maximum point or trace function until you reach the value for x Press ENTER Note: In this case, the maximum of the function on [–1, 2] is 5 and occurs at x = 0.