Question

Given f(x) = \frac (\sqrt ( x ) - 6 )(\sqrt ( x ) + 6 ).

Find f'( x ) = __________________

Find the equation of the tangent line when x = 25. No decimals allowed.
y = __________________

Answer 1

Just to avoid using the quotient rule:\[f(x)=\frac{\sqrt x-6}{\sqrt x+6}=\frac{\sqrt x+6-12}{\sqrt x+6}=1-12(\sqrt x+6)^{-1}\]

Answer 2

Refer to the attachment from the Mathematica computer program.