Calculus on the TI-84: Derivatives, Integrals & CALC Menu
Master calculus on your calculator with this calculus TI-84 guide: compute numerical derivatives with nDeriv(, definite integrals with fnInt(, and find zeros, minimums, maximums, and intersections using the CALC menu.
Quick answer: For derivatives, press MATH and choose nDeriv(, then type nDeriv(X^2,X,3) to get the derivative at x = 3. For integrals, use MATH → fnInt(, for example fnInt(X^2,X,0,2). For zeros, minimums, maximums, and intersections, graph the function, press 2ND + TRACE to open the CALC menu, and follow the left-bound / right-bound / guess prompts.
Numerical derivatives with nDeriv(
The TI-84 Plus CE does not do symbolic algebra — it approximates the derivative using numerical differentiation (see Wikipedia), which is plenty accurate for homework and exams.
- Press MATH and choose 8:nDeriv(.
- Type the expression, the variable, and the point, separated by commas: nDeriv(X^2,X,3).
- Press ENTER. The calculator returns 6, since the derivative of x² is 2x and 2(3) = 6.
The X key is X,T,θ,n. Because nDeriv( samples points near your x-value, answers at sharp corners or cusps are less reliable. Try it instantly on our free TI-84 calculator. Double-check sharp-corner results in any calculus TI-84 workflow.
Numerical integrals with fnInt(
- Press MATH and choose 9:fnInt(.
- Type the expression, the variable, the lower limit, and the upper limit: fnInt(X^2,X,0,2).
- Press ENTER. You get about 2.6667, which is 8/3.
Order matters: lower limit first, then upper. If your answer looks wrong, double-check the limits and make sure the function is typed exactly as intended.
The CALC menu: zeros, minimum, maximum, intersect
Graph the function first: press Y=, type your function (say Y1=X^2−4), and press GRAPH. Then press 2ND + TRACE to open the CALC menu. Every option below follows the same rhythm: set a left bound, a right bound, and a guess, pressing ENTER after each.
Finding a zero (x-intercept) — choose 2:zero. Move the cursor to the left of the root and press ENTER (Left Bound?), move it to the right and press ENTER (Right Bound?), then press ENTER once more (Guess?). For Y1=X^2−4 you will find zeros at x = −2 and x = 2 — run it once per root.
Finding a minimum or maximum — choose 3:minimum or 4:maximum and bracket the turning point the same way. For Y1=X^2−4, the minimum comes out at (0, −4).
Finding an intersection — graph both functions, for example Y1=X^2 and Y2=X+2. Choose 5:intersect, press ENTER on the first curve, ENTER on the second curve, move near the crossing for your guess, and press ENTER. You get (2, 4); run it again near the other crossing for (−1, 1).
dy/dx and shaded integrals on the graph
Two more CALC options are worth knowing. 6:dy/dx draws the tangent line at any point you pick and reports the numerical derivative there — a nice visual check of an nDeriv( answer. 7:∫f(x)dx shades the area under the curve between two x-values you choose and reports the integral, matching what fnInt( computes.
Mistakes to avoid
- Skipping the graph. The CALC menu only works from the graph screen — press GRAPH first, and make sure the function is turned on in the Y= editor.
- Bad bounds. For zeros, the function must actually change sign between your left and right bounds, or you get ERR:NO SIGN CHNG. Zoom in and bracket the root more tightly.
- Degree mode with trig. If your function uses sin, cos, or tan, switch to radians first: MODE → highlight Radian → ENTER.
- Forgetting it is numerical. nDeriv( and fnInt( approximate — they will not show steps, and they can misbehave at discontinuities and sharp corners.
More worked examples and troubleshooting live in our TI-84 guides hub. Bookmark this calculus TI-84 tutorial before your next exam.
Calculus TI-84: frequently asked questions
Why do I get ERR:NO SIGN CHNG when finding a zero?
The function does not change sign between your left and right bounds — move them closer around the crossing and try again.
Is nDeriv( exact?
No. It is a numerical approximation, extremely close for smooth functions but unreliable at cusps, corners, and discontinuities.
Can the TI-84 show calculus steps symbolically?
No — the TI-84 Plus CE computes numeric answers only. For step-by-step symbolic work you would need a CAS calculator or a computer algebra system.
My fnInt( answer looks wrong. What should I check?
Confirm the lower limit comes before the upper limit, the function matches what you graphed, and trig functions are in the right angle mode.
The CALC menu does nothing when I press 2ND + TRACE.
You are probably on the home screen instead of the graph. Press Y=, make sure your function is entered and turned on, then press GRAPH before opening CALC.
How do you find the derivative on a TI-84?
The TI-84 Plus CE does not do symbolic algebra — it approximates the derivative using numerical differentiation. Press MATH and choose 8:nDeriv(, then type the expression, the variable and the point separated by commas, for example nDeriv(X^2,X,3). Press ENTER: the calculator returns 6, since the derivative of x² is 2x and 2(3) = 6.
How do you calculate an integral on a TI-84?
Press MATH and choose 9:fnInt(. Type the expression, the variable, the lower limit and then the upper limit, for example fnInt(X^2,X,0,2). Press ENTER: you get about 2.6667, which is 8/3.
What does nDeriv( do on a TI-84?
nDeriv( numerically estimates the derivative of a function at a single x-value. You call it as nDeriv(function, X, value), for instance nDeriv(X^2,X,3) returns 6. It is unreliable at sharp corners or cusps, where the numerical estimate can be wrong.
What is the CALC menu on a TI-84 used for?
The CALC menu analyses graphs you have already drawn: graph your function with Y= and GRAPH first, then press 2ND + TRACE. Its options include 2:zero for roots, 3:minimum and 4:maximum for turning points, 5:intersect for where two graphs cross, 6:dy/dx for the derivative at a point, and 7:∫f(x)dx for the area under a curve. Most options ask you to set a left bound, a right bound and a guess, pressing ENTER after each.
