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Question

What is the equation of a normal line?


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Solution

Normal line:

The normal line is the line that is perpendicular to the tangent line at the point of tangency.

Let y=fx is the function of a curve.

Then, the slope of the normal line at x=x0 is the negative reciprocal of the derivative of the function,

The slope of the normal line =−1f'(x0)
Hence, the equation of the normal line at the point x0,y0 is,

y-y0=-1f'(x0)(x-x0)

Hence,the normal line is y-y0=-1f'(x0)(x-x0)


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