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

Answer 1

Elijah Abram

Use the derivative at that point.

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)#

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Answer 2

Emma Aldridge

To find the equation of a line normal to a curve, you need to follow these steps:

Determine the derivative of the curve to find its slope at a given point.
Find the negative reciprocal of the slope obtained in step 1. This will give you the slope of the line normal to the curve.
Identify the point on the curve where you want the line to be normal.
Use the point-slope form of a line (y - y₁ = m(x - x₁)) and substitute the values of the slope and the coordinates of the point from step 3.
Simplify the equation obtained in step 4 to its desired form, such as slope-intercept form (y = mx + b) or standard form (Ax + By = C).

This will give you the equation of the line that is normal to the curve at the specified point.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.