JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let a curve \(y=f(x), x \in(0, \infty)\) pass through the points \(P\left(1, \frac{3}{2}\right)\) and \(Q\left(a, \frac{1}{2}\right)\). 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 \(b c=3\), then \((P Q)^2\) is equal to \(.........\).
- A \(4\)
- B \(3\)
- C \(5\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
Equation of tangent at \(R(b, f(2))\) is \(y-f(b)=f^{\prime}(b) \cdot(x-b)\) which passes through \((0, c)\) \(\Rightarrow c - f ( b )= f ^{\prime}( b ) \cdot(- b )\) \(\Rightarrow \frac{3}{b}-f(b)= f ^{\prime}( b ) \cdot(- b )\)…
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