Calculus/Cal 2·tangent-line-equation

Tangent Line Equation

Enter f(x) and x₀. The calculator evaluates f(x₀) and f′(x₀), then returns y − f(x₀) = f′(x₀)(x − x₀). For f(x) = x² + 3 at x₀ = 1, it gives y − 4 = 2(x − 1).

Math animationCalculus/Cal 2 · tangent-line-equation

✓ All 3 test cases pass.

Inputs

Curve Function

The function representing the curve.

Point x-coordinate

The x-coordinate of the point where the tangent is evaluated.

Test cases

These cases run live in your browser every time the page loads. If any fail, the calculator is broken — file an issue.

#	Inputs	Expected	Got	Status
1	{"curve_function":"ln(x^2 - 8x + 1)","point_x":8}	8 $y = 8.0000(x - 8.0000)$	8 $y = 8.0000(x - 8.0000)$	✓
2	{"curve_function":"x^2 + 3","point_x":1}	2 $y - 4.0000 = 2.0000(x - 1.0000)$	2 $y - 4.0000 = 2.0000(x - 1.0000)$	✓
3	{"curve_function":"x^2","point_x":-2}	-4 $y - 4.0000 = -4.0000(x + 2.0000)$	-4 $y - 4.0000 = -4.0000(x + 2.0000)$	✓

APIDeveloper APICall this calculator from codeexpand ↓

Endpoint

POST/api/calculators/calculus-cal-2/tangent-line-equation/compute

Inputs (2)

curve_functionexpressiondefault "ln(x^2 - 8x + 1)"
point_xnumberdefault 8

Example

curl -sX POST http://localhost:3001/api/calculators/calculus-cal-2/tangent-line-equation/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"curve_function":"ln(x^2 - 8x + 1)","point_x":8}}'

Try it live

Edit the body below, then click Call API.

Request body

Response

(click Call API to see the response)

full API docs →

Source: Pattern from: Calculus II Final Exam Review.pdf. Reproduces a standard tangent-line-equation computation; problem text paraphrased.

AI disclosure: Calculator code generated by openai/gpt-4o-mini-2024-07-18; verified by 2 test cases.