Find the slope of a function at a point
Get the derivative of a function at one x value as a decimal, using the built-in derivative function.
The derivative at a point is the slope of the curve there. A calculator finds it numerically: it looks at the curve just left and right of the point and measures the slope between them.
You give it three things: the function, the variable, and the x value. The answer is very close to exact, but the last digit can be a hair off.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Open the MATH menu and choose item 8, the derivative function. It pastes nDeriv( on the screen.
math8Type the function X², then a comma, the variable X, a comma, and the point 3. Close the bracket.
X,T,θ,nx²,X,T,θ,n,3)Press enter. The slope of X² at 3 is 6.
enter
You should seenDeriv(X²,X,3) 6
Natural Scientific 991
Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.
Press SHIFT and the integral key to get the d/dx template.
SHIFTd/dx∫Type the function with the x key (ALPHA, then the bracket key), square it, then move right to the point box and type 3.
ALPHAx)x²▶3Press = to see the slope.
=
You should seed/dx(x²,3) 6
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
On the calculation screen open the MATH soft menu with the F4 key, then press F3 for d/dx.
F4F3Type X² with the X key, move right and type the point 3.
X,θ,Tx²▶3Press EXE for the slope.
EXE
You should seed/dx(X²,3) 6
Tips
- Only use this where the function is smooth. At a sharp corner, such as |x| at 0, the answer means little.
- If you see 3.000001 instead of 3, that is the numeric method, not a mistake. Round it.
Related guides
- Read the slope from a graphGraph a function and move to a point to see dy/dx, the slope of the curve there.
- Differentiate with a formula answerGet the derivative as an expression in x, not just a number at one point.
- Find the equation of a tangent lineUse the derivative to get the slope at a point, then build the line y = m(x − a) + f(a).