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How to find arc length and the maximum of a function on a TI-89 Titanium

By E-Code · updated

Press F3 8 for arcLen(, type the curve, the variable and the two ends and press ◆ ENTER: arcLen(x^2,x,0,1) gives 1.47894. F3 7 gives fMax( (F3 6 is fMin(), so fMax(-x^2+4x,x) ENTER gives x = 2.

Step by step

  1. Pick arcLen(. F3 8 Press F3 for Calc, then 8 for arcLen(, the length along a curve.
  2. Type x^2, x, 0, 1. X ^ 2 , X , 0 , 1 ) Type x^2, x, 0, 1 and ). That is: the curve, the letter, then where it starts and ends.
  3. Get a decimal. ◆ ENTER Press ◆, then ENTER. ◆ ENTER gives a decimal instead of a long exact answer.
  4. Pick fMax(. F3 7 Press F3, then 7 for fMax(. It finds where a function is biggest. fMin( (F3 6) finds where it is smallest.
  5. Type -x^2+4x, x. (-) X ^ 2 + 4 X , X ) Press (-) for the minus sign, then type x^2+4x, a comma, x and ).
  6. Find the peak. ENTER Press ENTER.
  7. Read both answers. The curve y = x² from 0 to 1 is 1.47894 long, and -x²+4x is biggest at x = 2.

What the screen shows

The curve y = x² from 0 to 1 is 1.47894 long, and -x²+4x is biggest at x = 2.

Look for x = 2 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-89 calculator and each key lights up in turn as you press it.

Try “Find arc length and the maximum of a function” on the TI-89 calculator

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Math programs for the TI-89 Titanium:

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