The normal to the curve at the point is parallel to the straight line.Find the equation of the tangent to the curve at the point
If this is how your post should have read, then calculating the derivative of
will give you the slope of the tangent.
The slope of the line
is
The normal and the tangent are perpendicular, so you can find what the tangent slope needs to be.
The derivative being equal to this tangent slope will obtain the x co-ordinate of
The y co-ordinate is obtained by placing the x co-ordinate into f(x).
Finally, to get the equation of the tangent, use the equation of the line formula,
using the slope calculated and the co-ordinates of