What is the equation of the normal line

Ariel Collier

Ariel Collier

Answered question

2022-04-09

What is the equation of the normal line of f(x)=exx3 at x=0?

Answer & Explanation

Assorrymarf0cgr

Assorrymarf0cgr

Beginner2022-04-10Added 10 answers

Given f(x)=exx3
Then f(x)=ex3x2
f(0)=e00=1
So the graph of the function passes through (0,1)
f(0)=e00=1
So the slope of the tangent at (0,1) is 1.
If the slope of the tangent is m then the slope of the normal is 1m. So in our example the slope of the normal is 11=1
The equation of a line of slope m passing through a point (x0,y0) can be written as:
(yy0)=m(xx0)
In our case we have (x0,y0)=(0,1) and m=-1, so:
(y-1)=-1(x-0)=-x
That is y=-x+1 in slope intercept form.

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?