How do you find the equation of the tangent line

Cassidy Johnson

Cassidy Johnson

Answered question

2022-02-12

How do you find the equation of the tangent line to the curve y=2x+1x+2 at the given point (1,1)?

Answer & Explanation

Rachel Frazier

Rachel Frazier

Beginner2022-02-13Added 14 answers

We have, y=2x+1x+2
Now, the derivative (using quotient rule)
dydx=2(x+2)(2x+1)(x+2)2=3(x+2)2
Now dydx at (1,1) is the slope of the tangent to the curve at (1,1)
m=(dydx)1,1=39=13
Now, point-slope form a straight line is given by
(yy1)=m(xx1)
Now, (x1,y1)=(1,1) and m=13, substituting these values in above equation we get,
y1=13(x1)y=x3+23 (Answer)

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