How do you find the equation of the

Jayleen Aguirre

Jayleen Aguirre

Answered question

2022-04-15

How do you find the equation of the tangent and normal line to the curve y=1x3 at (2,18)?

Answer & Explanation

Mey9ci0

Mey9ci0

Beginner2022-04-16Added 14 answers

To find the slope of the tangent line, mt, we compute  dy  dx  and then evaluate it at
x=2
 dy  dx =3x4
mt=324=316
The slope of the normal line, mn, can be found using the following equation:
mn=1mt
mn=1316
mn=163
Using the point-slope form of the equation of a line, we find that the equation of any line passing through the point (2,18) is:
y=m(x2)+18 [1]
Substitute the value of mt into equation [1], to obtain the equation of the tangent line:
y=316(x2)+18
Substitute the value of mn into equation [1], to obtain the equation of the normal line:
y=163(x2)+18

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?