Optimisation and root questions become a couple of button presses.
In short: A maximum, minimum or zero of a graph is found with the calculator's graph-analysis tools after you draw the function. You select the tool, set a left and right bound around the point, and the GDC returns its coordinates. Use it when a question asks for the maximum, the turning point or where the graph crosses the x-axis.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | 2nd → CALC → 2:zero, 3:minimum or 4:maximum; set a left bound, right bound, then guess. | G-Solve (SHIFT F5) → ROOT, MIN or MAX. | menu → Analyze Graph → Zero, Minimum or Maximum. |
Tip: For a turning point, minimum/maximum gives both the x and y values you usually need.
Tip: For a turning point, minimum/maximum gives both the x and y values you usually need.
Tip: For a turning point, minimum/maximum gives both the x and y values you usually need.
Here's a real IB-style question that uses exactly this technique.
The height of a ball is modelled by h(t) = −(t − 2)² + 9, for t ≥ 0. Find the maximum height and the time at which it occurs.
Optimisation and root questions become a couple of button presses. An optimisation question asks for the maximum or minimum value of a modelled quantity. Finding the roots (zeros) of a function that doesn't factorise nicely.
1. Graph the function with a window that shows the feature you want. 2. 2nd → CALC → 2:zero, 3:minimum or 4:maximum; set a left bound, right bound, then guess. 3. Note the coordinates shown at the bottom of the screen.
1. Graph the function with a window that shows the feature you want. 2. G-Solve (SHIFT F5) → ROOT, MIN or MAX. 3. Note the coordinates shown at the bottom of the screen.
1. Graph the function with a window that shows the feature you want. 2. menu → Analyze Graph → Zero, Minimum or Maximum. 3. Note the coordinates shown at the bottom of the screen.
For a turning point, minimum/maximum gives both the x and y values you usually need.
In the worked example on this page (3 marks, Paper 2), the marks are: M1: Graph h(t), use the maximum tool; A1: Maximum 9 m; A1: at t = 2 s.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.