What is the equation of the tangent line

Sandra Cain

Sandra Cain

Answered question

2022-03-16

What is the equation of the tangent line of y=xx2 at x=1?

Answer & Explanation

Ettrapinithr

Ettrapinithr

Beginner2022-03-17Added 7 answers

Let f(x)=xx2
f(1)=1-1=0
So the curve passes through the point (1,0)
f'(x)=1-2x and f'(1)=1-2=-1
So the slope of the tangent at (1,0) is -1.
In slope intercept form, the equation of the tangent line may be written:
y=mx+c
where the slope m=-1 and c is a constant to be determined.
We also know that this tangent line passes through (1,0) so the equation is satisfied by this pair of values for x and y.
Hence c=y-mx=0-(-1)(1)=1
and we can write the equation of the line as:
y=-x+1
or simply:
y=1-x

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?