find an equation of the tangent line to the curve at the given point y=x+tanx (pi)(2pi)

Question

Please help me 

Answer 1

Jessica,

 

To find the equation of the tangent line we need a point (pi,2pi) and a slope. The slope can be found by plugging in pi into y'=1+(sec x)^2

 

sec pi=1/(cos pi)=-1

so y' at (pi,2pi)=1+(-1)^2=2

 

Now we know slope m=2=(y2-y)/(x2-x)=(2pi-y)/(pi-x)

2pi-2x=2pi-y

y=2x

 

Hope that helps!