Gives a gradient instantly to check your differentiation or when a function is awkward.
In short: A numerical derivative gives the gradient of a function at a single point without differentiating by hand. You enter the function and the x-value, and the GDC returns an approximate value of f′(x). Use it to check an algebraic derivative, or when a question allows calculator methods for the gradient at a point.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | MATH → 8:nDeriv(, then enter nDeriv(f(x), x, a). Or graph and use 2nd → CALC → 6:dy/dx. | Run-Matrix → MATH (F4) → d/dx, then enter the function and the x-value. | menu → Calculus → Numerical Derivative at a Point. |
Tip: Handy for checking the gradient at a point or finding a tangent's slope.
Tip: Handy for checking the gradient at a point or finding a tangent's slope.
Tip: Handy for checking the gradient at a point or finding a tangent's slope.
Here's a real IB-style question that uses exactly this technique.
For f(x) = x³ − 2x, find f′(2).
Gives a gradient instantly to check your differentiation or when a function is awkward. Checking a derivative you found algebraically, especially for an awkward function. The function is too messy to differentiate by hand in the time available.
1. MATH → 8:nDeriv(, then enter nDeriv(f(x), x, a). Or graph and use 2nd → CALC → 6:dy/dx. 2. Read off the gradient - useful for tangent slopes without algebra.
1. Run-Matrix → MATH (F4) → d/dx, then enter the function and the x-value. 2. Read off the gradient - useful for tangent slopes without algebra.
1. menu → Calculus → Numerical Derivative at a Point. 2. Read off the gradient - useful for tangent slopes without algebra.
Handy for checking the gradient at a point or finding a tangent's slope.
In the worked example on this page (2 marks, Paper 2), the marks are: M1: nDeriv of x³ − 2x at x = 2; A1: 10.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.