Determine the equation for the tangent to the curve at...

[JSmith]

Determine the equation for the tangent to the curve

at x =

.

Is that correct?? Thanks!

 

[DrPhil]

Determine the equation for the tangent to the curve

at x =

.
View attachment 2887
Is that correct?? Thanks!

It's (approximately) correct, but I would prefer the exact solution using \(\displaystyle \tan(\pi /3) = \sqrt{3}\):

\(\displaystyle \displaystyle y(x) = -3\ x + \left(\dfrac{4 \pi}{3} - \sqrt{3}\right) \)