Get the gradient at a point - and the tangent's equation - straight off the graph.
In short: Drawing a tangent on a GDC means placing a tangent line at a chosen x-value on a graph and reading its equation or gradient. The tangent's gradient is the derivative at that point. Use it to check a differentiation answer, or to find the gradient at a point where doing it by algebra would be slow.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | 2nd → PRGM (DRAW) → 5:Tangent(, type the x-value (or move the cursor), ENTER - the tangent and its equation appear. | With the graph shown, SHIFT → F4 (Sketch) → Tangent, then enter the x-value. | Use the derivative template to evaluate f′(a), or draw a tangent with the Geometry tools. |
Tip: The gradient shown equals the derivative at that point - a fast check on your differentiation.
Tip: The gradient shown equals the derivative at that point - a fast check on your differentiation.
Tip: The gradient shown equals the derivative at that point - a fast check on your differentiation.
Here's a real IB-style question that uses exactly this technique.
For f(x) = x², find the gradient of the tangent at x = 3.
Get the gradient at a point - and the tangent's equation - straight off the graph. A question asks for the gradient of a curve at a specific point. Finding the equation of the tangent line at a given point.
1. Graph the function with the point on screen. 2. 2nd → PRGM (DRAW) → 5:Tangent(, type the x-value (or move the cursor), ENTER - the tangent and its equation appear. 3. The displayed line gives both the gradient and the tangent's equation.
1. Graph the function with the point on screen. 2. With the graph shown, SHIFT → F4 (Sketch) → Tangent, then enter the x-value. 3. The displayed line gives both the gradient and the tangent's equation.
1. Graph the function with the point on screen. 2. Use the derivative template to evaluate f′(a), or draw a tangent with the Geometry tools. 3. The displayed line gives both the gradient and the tangent's equation.
The gradient shown equals the derivative at that point - a fast check on your differentiation.
In the worked example on this page (2 marks, Paper 2), the marks are: M1: Draw the tangent at x = 3; A1: Gradient = 6.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.