Question

How do you find the normal line of a function?

Answer 1

Finding the normal line of the function:

The function and the tangent line intersect at the point of tangency.

The line which passes through this point of contact and is perpendicular to the tangent line is called the normal line.

Suppose $f\left(x\right)$is a function such that the slope of a tangent line is $m=f\text{'}\left(x\right).$

Therefore, the slope of a normal line is $-\frac{1}{m}$.

Now the equation of the normal line will be the equation of a line with slope $-\frac{1}{m}$ and passing through the point of tangency.

Hence, in this way, we can find the normal line of a function.