Find an equation of the tangent line to the curve

Sam Longoria

Sam Longoria

Answered question

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

Beginner2021-12-22Added 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

Beginner2021-12-23Added 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

Expert2021-12-28Added 777 answers

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

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