Analyze function values near a target point. Compare one-sided slopes and continuity with practical tolerances. Export tables, inspect classifications, and study non smooth behavior.
| Case | x₀ | h | f(x₀-h) | f(x₀) | f(x₀+h) | Expected Reading |
|---|---|---|---|---|---|---|
| |x| at 0 | 0 | 0.001 | 0.001 | 0 | 0.001 | Sharp corner |
| x² at 1 | 1 | 0.001 | 0.998001 | 1 | 1.002001 | Likely differentiable |
| Jump sample | 0 | 0.001 | 1 | 0 | 2 | Discontinuous |
| Time | x₀ | h | f(x₀-h) | f(x₀) | f(x₀+h) | Left slope | Right slope | Central slope | Classification |
|---|---|---|---|---|---|---|---|---|---|
| No calculations saved yet. | |||||||||
This calculator estimates one-sided derivatives from nearby values.
Left derivative approximation:
DL ≈ [f(x₀) - f(x₀ - h)] / h
Right derivative approximation:
DR ≈ [f(x₀ + h) - f(x₀)] / h
Central slope approximation:
DC ≈ [f(x₀ + h) - f(x₀ - h)] / (2h)
A point is treated as likely differentiable when the function looks continuous and the gap |DL - DR| stays within the slope tolerance.
If continuity fails, differentiability also fails. If slopes are very steep or disagree, the point may be a corner, cusp, or vertical tangent.
A non differentiable function calculator helps you inspect difficult points fast. Many functions look smooth across most inputs. Some points behave very differently. A graph may show a corner. Another may hide a cusp. Some points become undefined because continuity fails. This calculator gives a practical test using nearby values.
The tool compares left and right derivative estimates around a target point. It also checks whether nearby function values stay close to the center value. That matters because differentiability usually requires continuity first. When one-sided slopes agree, the point is likely differentiable. When they disagree, the function may be non smooth at that point.
The classification logic is built for real numeric work. If sampled values break continuity, the result points to discontinuity. If the slopes are finite but unequal, the point likely has a corner or kink. If the slopes become very large, the tool can flag a vertical tangent or cusp. This makes the output useful for calculus homework, exam review, and quick numerical checks.
Use a small step size. Very large steps can hide local behavior. Very tiny steps can magnify rounding noise. Start with a moderate value such as 0.001. Then test smaller values and compare the outcome. Stable patterns usually give stronger confidence. This approach works well for piecewise functions, absolute value models, and sampled data from tables.
Students use this calculator to study corners, cusps, and continuity. Teachers use it for examples. Engineers and analysts can test measured data near a transition point. The export options also help when you need a saved record. The example table, formula section, and FAQs make the page useful for learning and repeated practice.
It estimates left and right derivatives near one point. Then it checks continuity and compares the slopes. The output flags likely differentiable points, corners, cusps, vertical tangents, or discontinuities.
It gives a strong numerical indication, not a formal proof. For exact proof, combine the result with symbolic work, limits, or a rigorous definition from calculus.
The center value helps estimate both one-sided derivatives and continuity. Without it, the calculator cannot compare how the function behaves as you approach the target point.
Start with a small positive value such as 0.001. Then try smaller values and compare the classifications. Stable results usually mean your estimate is more reliable.
Slope tolerance is the allowed gap between left and right derivative estimates. A smaller tolerance is stricter. A larger tolerance is more forgiving with noisy or rounded data.
It controls how close the nearby sampled values must stay to the center value. If the gaps are too large, the point is treated as likely discontinuous.
Yes. It works well for piecewise rules when you already know the function values on both sides of the target point. That makes corner and discontinuity checks easy.
They export the calculation history table on the page. This is useful for saving test runs, comparing cases, or sharing your numerical analysis with others.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.