Differential Calculus Calculators
This category presents calculators describing rates of change and the behaviour of mathematical functions. Each tool provides numerical outputs for limits, derivatives, curvature properties and other relationships that appear in differential calculus.
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Critical Points and Extrema Calculator
A quadratic expression reaches a highest or lowest turning point that depends on the values of its three coefficients.
Example use: Noting where a curved path on a simple sketch reaches its lowest point before rising again.
Inputs: three coefficients written in plain numbers
Outputs: function type, stationary point, extrema value, classification, discriminant, range, vertical intercept, interval of increase, interval of decrease
Visual: shows the overall curve with the stationary point marked clearly
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Implicit Differentiation Calculator
A curve defined by a mixed expression in two variables has a slope at any chosen point that depends on how each part of the expression changes.
Example use: Checking the slope of a curved outline at a particular spot on a hand-drawn diagram.
Inputs: coefficients for the squared terms, the mixed term, the single-variable terms, the constant term, and the point of interest written as horizontal and vertical values
Outputs: partial derivative with respect to the horizontal variable, partial derivative with respect to the vertical variable, overall slope, tangent line equation, normal line equation
Visual: shows the curve with the tangent and normal lines drawn through the chosen point
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Limit Calculator (Quadratic Functions)
A quadratic expression approaches a specific value as its input moves closer to a chosen point, and its slope at that point is fixed by its coefficients.
Example use: Estimating the value a smooth curve is heading towards near a particular position on a sketch.
Inputs: three coefficients written in plain numbers and the point being approached
Outputs: limit value at the chosen point, slope at that point
Visual: shows the curve with the tangent line and the point being approached highlighted
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Second and Higher-Order Derivative Calculator
A quadratic expression has a constant second derivative, a single turning point, and a predictable shape determined by its coefficients.
Example use: Checking how sharply a smooth curve bends at a particular position on a simple drawing.
Inputs: three coefficients written in plain numbers and the evaluation point
Outputs: function value, first derivative, second derivative, discriminant, vertex, tangent line at the evaluation point
Visual: shows the curve, its first and second derivative curves, and the tangent line at the chosen point
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Tangent and Normal Line Calculator
A smooth curve has a single straight line that touches it without cutting through at a chosen point, and another straight line that meets it at a right angle.
Example use: Marking the direction of a curve at a specific point when sketching a smooth outline.
Inputs: three coefficients written in plain numbers and the point of interest
Outputs: point of tangency, tangent slope, tangent equation, normal slope, normal equation, curvature, radius of curvature
Visual: shows the curve with both the tangent and normal lines drawn through the selected point
Differential Calculus Calculators FAQs
Differential calculus examines rates of change and the behaviour of functions. It describes how values vary as inputs move across different positions.
Limits describe the value a function approaches near a specific point. They form the basis for defining continuity and derivatives, allowing us to analyse behaviour even when a function is not defined at that exact location.
Higher-order derivatives describe concavity, curvature and inflection behaviour. They show how a function bends, accelerates or changes direction across its domain.
The derivative at a point gives the slope of the tangent line. It represents the instantaneous rate of change for the function at that specific position.