Dawnbridge

Casio fx-CG50 field manual for IB Math

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17

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/48x2.

1

From the MAIN MENU open Graph (icon 5) and type the function on Y1: for the e^▯ template, type , then to leave the exponent box; after that type . Press to register it.

2

Frame the graph on the standard window: (V-Window) → (STANDRD), then and (DRAW). Both turning points are on screen, but the y-range is much taller than the actual height of the curve, so the maximum and minimum are harder to read precisely.

RadNorm2
Real
3

Zoom in on the part that matters with a box: press (Zoom) → (BOX). Move the cursor above-left of the curve's turning points and press to anchor the first corner; move below-right of them and press again. The dashed marquee shows the region the window will snap to. Make sure it contains both the peak and the valley.

RadNorm2
Real
4

The window snaps to the box. Press (G-Solv) → (MAX). The calculator jumps to the local maximum and prints the coordinates along the bottom.

[EXE]:Show coordinates
Y1=eX/4X2/8
MAX
X=1.42961187Y=1.17413808
5

Then press (G-Solv) → (MIN) to jump to the local minimum. If a graph ever shows more than one candidate of the same type, use and to move between them.

[EXE]:Show coordinates
Y1=eX/4X2/8
MIN
X=8.6131695Y=-0.660166554
Result

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

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/36x2.

  2. 2

    Find the coordinates of the local maximum and local minimum of f(x)=12x3x+ln(x+5).

  3. 3

    Find the coordinates of the local maximum and local minimum of f(x)=10x3x+ex/5.