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How to find the maximum or minimum of a graph on a TI-84 Plus CE, TI-84 Plus or TI-83 Plus

By E-Code · updated

Graph the function, press 2nd CALC (above TRACE) and 4 for maximum (3 for minimum), then type a left bound, ENTER, a right bound, ENTER, and ENTER at Guess. The calculator shows the X and Y of the top or bottom.

Before you start

Type the function into the Y= editor first: this guide uses Y1 = −X² + 4X (Y=, (−), X,T,θ,n, x², +, 4, X,T,θ,n, then 2nd QUIT).

Y= (-) X,T,θ,n X² + 4 X,T,θ,n 2nd MODE

Step by step

  1. Draw the graph. GRAPH Press GRAPH. Y1 = −X² + 4X is already typed in for you: a hill.
  2. Open CALC. 2nd TRACE Press 2nd, then TRACE for CALC.
  3. Pick maximum. 4 Press 4 for maximum (3 is minimum, for a valley). It asks for a left bound.
  4. Left of the top. 0 Type 0.
  5. Confirm the left bound. ENTER Press ENTER.
  6. Right of the top. 4 Type 4. The top of the hill is between 0 and 4.
  7. Confirm the right bound. ENTER Press ENTER. Now it asks for a guess.
  8. Find the maximum. ENTER Press ENTER to take the cursor's spot as the guess.
  9. Read the top. The top is at X = 2, Y = 4. The X may show as 1.9999…: the calculator searches in tiny steps.

What the screen shows

The top is at X = 2, Y = 4. The X may show as 1.9999…: the calculator searches in tiny steps.

Look for Y=4 on the screen.

Try it with the keys lit up

This guide is one of E-Code's Learn lessons. Open it on E-Code's TI-84 calculator and each key lights up in turn as you press it.

Try “Find the maximum or minimum of a graph” on the TI-84 calculator

Related

Math programs for the TI-84 Plus CE:

All TI-84 algebra guides · All TI-84 guides · All calculator guides