Nested Squareroot
Calculus
Level
2
Consider the function
\( f(x) = \sqrt{x+\sqrt{x+\sqrt{x+\ldots}}} \)
If the gradient of the tangent of the function at \( x = 12 \) can be expressed as \( \frac{a}{b} \) where \( a \) and \( b \) are positive coprime integers, what is the value of \( a + b \).
by
Cole Coupland