Question

Let a curve y = f(x), x ∈ (0, ∞) pass through the points  \(p ( 1\frac{3 }{2} )\) and  Q \( ( a,\frac{1 }{2} )\). If the tangent at any point R(b, f(b)) to the given curve cuts the y-axis at the point S (0, c) such that bc = 3, then (PQ)² is equal to ______.

Answer 1

Correct Answer: 5

We are given the equation of the tangent at point R: \[ y - f(b) = f'(b)(x - b) \] By solving for the points \(P\) and \(Q\), we find that \(PQ^2 = 5\).