Tangent Line Calculator

The tangent line at a point is the straight line through that point with the same slope as the curve, and it is also the linear approximation used to estimate nearby values. Choose a cubic with its coefficients, or one of seven standard forms such as a power, an exponential, a logarithm, a sine or a reciprocal, then give the point of tangency. You get the derivative in closed form, the point, the slope, the tangent line in both slope-intercept and point-slope shape, the perpendicular normal line, and a comparison of the linear estimate against the true value at a nearby x. There is no algebra system behind this, so it will not differentiate an expression you type: the menu exists because every derivative on it was worked out by hand once and is therefore right every time.

Calculator Type

f(x) = a x^3 + b x^2 + c x + d. Leave a coefficient at zero to drop that term, so a quadratic is just a = 0.

a, the x^3 coefficient

b, the x^2 coefficient

c, the x coefficient

d, the constant

x, the point of tangency *

x for the linear estimate

A value near the point of tangency. The page compares the tangent line's estimate there against the real curve.

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Pick a form, set its parameters, and get the tangent at your point. Angles are in radians.

Function Form

a, the outer coefficient

b, the coefficient of x inside

Not used by the power form, which uses n instead.

c, the constant inside

Not used by the power form.

n, the exponent

Used by the power form only. It may be negative or fractional, but a fractional exponent needs a positive x.

x, the point of tangency *

x for the linear estimate

A value near the point of tangency, and inside the function's domain.

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