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Find the y-intercept?

 

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

The answer is 33/7.

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
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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