Question

How do you find the equation of a tangent line to a curve?

Answer 1

There is no short answer since this is a general question.

You must have a differentiable function to find a tangent line to a curve.

So, let `f(x)` be the function for the curve.
And let `f'(x)` be the derivative of `f(x)`.
Finally, let `x=a` be the value at which we want the tangent line:

`T(x)=f(a)+f'(a)(x-a)`

Note that this is also the formula for linear approximation functions.

There are many examples of tangent line and linear approximation problems, so just search for them.