Equation of a tangent to a curve

You must have a general understanding of graph gradients, tangents, normals and derivatives. This would probably be a reminder rather than a lesson. Finding the equation of a tangent to a curve involves finding the derivative/gradient function of the function and then finding the gradient m of the tangent at the given point and by substituting in the x-coordinate of the point in the derivative. So the steps are;

• Find the derivative f ’(x)
• Find the gradient m of the tangent by substituting in the x-coordinate of the point.
• And then use the following formula to get the equation of the tangent. You will need the m which is the gradient, x-coordinate which is the given value and the y-coordinate, you find this by substituting it in the original function.

You might be required or for your purpose to write the equation of the tangent in this form;

And that’s how you find the equation of a tangent. It’s that easy…

Read more about tangents here