TI-Nspire CX II field manual for IB Math
Finding maxima and minima
Graph a function, tighten the viewing window around the turning points, then use the calculator's maximum and minimum tools to read each coordinate.
Find the local maximum and local minimum of y=ex/4−8x2.
Open the Scratchpad's Graph view ( → B: Graph Scratchpad) and enter the function on f1(x)=. Press for the e^▯ template, type , press to leave the exponent box, then type . Press to register the graph.
Start on the standard window: → 4: Window/Zoom → 5: Zoom-Standard. Both turning points are visible already, but the graph uses a much taller y-range than it needs, so the turning points are visually compressed.
Zoom in on the part that matters with a box: → 4: Window/Zoom → 2: Zoom-Box. Click once above-left of the curve's turning points to anchor the first corner, then move below-right of them and click again. The dashed marquee shows the region the window will snap to. Make sure it contains both the peak and the valley.
Find the peak with → 6: Analyze Graph → 3: Maximum. At lower bound? move just left of the turning point and press ; at upper bound? move just right and press . The located maximum appears with its coordinates.
Now find the valley with → 6: Analyze Graph → 2: Minimum. At lower bound? move just left of the turning point near x≈8.61 and press ; at upper bound? move just right and press . The located minimum appears with its coordinates.
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
Find the coordinates of the local maximum and local minimum of f(x)=ex/3−6x2.
- 2
Find the coordinates of the local maximum and local minimum of f(x)=12x3−x+ln(x+5).
- 3
Find the coordinates of the local maximum and local minimum of f(x)=10x3−x+ex/5.