Build tangent equations from function values and derivatives. Check slope form, point form, and intercepts. Download neat outputs for homework, revision, reporting, and practice.
| Function | x₀ | f(x₀) | f'(x₀) | Tangent line |
|---|---|---|---|---|
| f(x) = x² | 2 | 4 | 4 | y = 4x - 4 |
| f(x) = 3x³ + 2 | 1 | 5 | 9 | y = 9x - 4 |
| f(x) = eˣ | 0 | 1 | 1 | y = x + 1 |
| f(x) = ln(x) | 1 | 0 | 1 | y = x - 1 |
The tangent line at x = x₀ uses the derivative as slope. First compute y₀ = f(x₀). Then compute m = f'(x₀). The point-slope equation is y - y₀ = m(x - x₀). The slope-intercept form is y = mx + b, where b = y₀ - mx₀.
The linear approximation is also useful. It is L(x) = f(x₀) + f'(x₀)(x - x₀). This gives a local estimate near the chosen point. For the normal line, the slope is -1/m when m is not zero.
Select a function family first. Enter the needed coefficients. Then enter the x value where the tangent touches the curve. Add a small dx if you want a local linear estimate. Press the calculate button. The tool will show the tangent equation, point of tangency, slope, angle, intercepts, and normal slope.
Use the export buttons after calculation. CSV is good for records and worksheets. PDF is useful for reports, printing, and sharing. Check the domain note when using logarithmic functions because the inside value must stay positive.
A tangent line shows how a curve behaves at one exact point. It touches the graph and shares the same instantaneous slope there. This calculator helps students, teachers, and analysts build that line quickly. It handles several common function families in one place.
You can work with polynomial, power, exponential, logarithmic, sine, and cosine functions. That makes the tool useful for many algebra and calculus tasks. Instead of solving each step by hand, you enter coefficients and a target x value. The calculator then evaluates the function and its derivative at that point.
The result block gives more than only the final equation. It also returns the point of tangency, derivative value, normal slope, intercepts, and the line angle. These extra outputs help with checking homework, verifying manual work, and understanding graph behavior. A linear approximation is included too. That part is valuable when you need a close estimate near the selected point.
The structure is practical for classroom use. Results appear above the form after submission, so the answer is visible immediately. The input area stays organized in a responsive grid. On large screens, it uses three columns. On smaller screens, it adjusts cleanly. On mobile, it becomes one column for easier entry.
The example table gives quick reference values for familiar functions. The formula section explains the math behind the tangent line. The usage section shows the working order. Export buttons let you save the outcome as CSV or PDF. That is useful for revision sheets, assignments, and project records.
This page keeps the design simple. It uses very little CSS, no color styling, and plain HTML FAQ content. The focus stays on calculation, clarity, and readable mathematical output. If you want a reliable tangent line equation tool with guided results, this file is a strong starting point.
A tangent line touches a curve at one point and matches the curve’s instantaneous slope there. It gives the best local straight-line approximation near that point.
The derivative gives the slope of the curve at the chosen x value. That slope becomes the slope of the tangent line.
Yes. The calculator supports sine and cosine forms with adjustable coefficient, frequency, and phase shift values.
The tool checks the logarithm domain. If the inside value is not positive, it shows an error instead of a misleading answer.
The normal line is perpendicular to the tangent line at the same point. Its slope is the negative reciprocal of the tangent slope, when defined.
Linear approximation uses the tangent line to estimate nearby function values. It works best close to the selected point of tangency.
Yes. You can download a CSV file for spreadsheet use and a PDF file for printing, sharing, or archiving.
Yes. It helps connect derivatives, slope, local behavior, and line equations in one practical workflow.
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.