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

1 Answer
Sep 1, 2014

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:


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.