Question

How you would find the equation of a line normal to a curve?

Answer 1

Use the derivative at that point.

Explanation:

Let the point be `(x_1,y_1)`, of the function `y=f(x)`.

Let the slope of tangent at `(x_1,y_1)` be `m`.
Then `m=dy/dx` at `(x_1,y_1)`.

Then the slope of normal is `-1/m`.

Hence the equation of the normal is

`y-y_1=-1/(dy/dx)(x-x_1)`