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

Question

Ezra Adams · Accepted Answer

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.

Cameron Alexander · Answer

undefined To find the equation of a tangent line to a curve, follow these steps:

1. Determine the point on the curve where the tangent line is desired.
2. Find the derivative of the curve's equation.
3. Substitute the x-coordinate of the point into the derivative to find the slope of the tangent line.
4. Use the point-slope form of a line (y - y₁ = m(x - x₁)) and substitute the slope and the coordinates of the point to obtain the equation of the tangent line.