Dawnbridge

TI-84 Plus CE field manual for IB Math

Everyone · 15 of 41

15

Finding maxima and minima

All courses

Graph a function, tighten the viewing window around the turning points, then use the calculator's maximum and minimum tools to read each coordinate.

Goal

Find the local maximum and local minimum of ​y=ex/4−8x2​.

1

Press and type the function on Y1: .

2

Start on the standard window: press (6: ZStandard). Both turning points are already visible on screen.

NORMALFLOATAUTOREALRADIANMP
3

Find the peak: press (4: maximum). At Left Bound? move just left of the peak and press ; at Right Bound? move just right of it and press . The shaded band shows the region being searched.

NORMALFLOATAUTOREALRADIANMP
4

At Guess? move near the peak and press . The cursor jumps to the maximum and its coordinates print at the bottom of the screen.

NORMALFLOATAUTOREALRADIANMP
Maximum
X=1.429611881 Y=1.174138079
5

Now the valley: press (3: minimum). At Left Bound? move just left of the valley and press ; at Right Bound? move just right of it and press ; at Guess? move near the valley and press . The calculator jumps to the minimum and prints its coordinates.

NORMALFLOATAUTOREALRADIANMP
Result

The local maximum is approximately ​(1.43,1.17)​ and the local minimum is approximately ​(8.61,−0.660).

NORMALFLOATAUTOREALRADIANMP
Minimum
X=8.613169519 Y=-0.6601665542

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Find the coordinates of the local maximum and local minimum of ​f(x)=ex/3−6x2​.

  2. 2

    Find the coordinates of the local maximum and local minimum of ​f(x)=12x3​−x+ln(x+5).

  3. 3

    Find the coordinates of the local maximum and local minimum of ​f(x)=10x3​−x+ex/5.