Normals

L3CALC

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Tangents to the graph of the functions can be found with the original function’s equation, and a point. That’s it. You first find the gradient of the tangent of the equation at that certain point, then get the equation of that tangent.

Normals are very similar to tangents. (kind of explained in L2CoordGeo) They are lines that are perpendicular to the tangent lines.

As explained in L2 Coordinate Geometry, to find the gradient of the line that’s perpendicular, we must flip the sign, AND the number. If we have a gradient of a tangent that’s $5$, then we first flip the sign into:

$$-5$$

Then we flip the number. The number above can be also written as:

$$\frac{-5}{1}$$

So, we flip it:

$$-\frac{1}{5}$$

If the gradient of the tangent is 5, then the gradient of the normal is $-\frac{1}{5}$.

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