Find the y-intercept?

Question

 

Find the y-intercept of the tangent line to the curve y=sqrt(x^2+33).

The answer is 33/7.

Answer 1

 

y=sqrt(x^2+33)

y' = 2x/[2sqrt(x^2+33)] = 4/7 at x = 4 (Attn: You need to give the point (4, 7))

Equation of tangent line at (4,7),

y - 7 = (4/7)(x-4)

Let x = 0. You have

y-int = 7+(4/7)(-4) = 33/7 <==Answer