Find an equation of the tangent line to the curve at the given point. y=x(81,9)

Sam Longoria

Sam Longoria

Answered

2021-12-21

Find an equation of the tangent line to the curve at the given point.
y=x(81,9)

Answer & Explanation

Edward Patten

Edward Patten

Expert

2021-12-22Added 38 answers

Step 1
Consider the given function:
y=x
Step 2
Now differentiate the function to find the slope.
dydx=12x
Step 3
Now find the slope at given point (81,9).
m=dydx(81,9)=1281
=118
Step 4
Write the equation for a line.
yy1=m(xx1)
Step 5
Put the values of known quantities.
y9=118(x81)
18y162=x81
x18y+81=0

Laura Worden

Laura Worden

Expert

2021-12-23Added 45 answers

Step 1
Let f(x)=x
Then, by Eq. 3, the slope of the tangent at (1,1) is
m=limh0f(81+h)f(9)h=limh081+h9h
=limh0(81+h9)(81+h+9)h(81+h+9)=limh081+h9h(81+h+9)
=limh0hh(81+h+9)=limh0181+h+9=118
Using the point-slope form of the equation of a line, we find that an equation of the tangent at the point (1,1) is
y9=118(x81)
Which simplifies to x18y+81=0

nick1337

nick1337

Expert

2021-12-28Added 573 answers

Thanks for the help, without you I would not have figured it out

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

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

Didn't find what you were looking for?