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JEE Mains · Maths · STD 12 - 6. Application of derivatives
A tangent to the curve, \(y\, = f(x)\) at \(P(x,y)\) meets \(x-\) axis at \(A\) and \(y-\) axis at \(B\). If \(AP : BP\,= 1: 3\) and \(f(a)\, = 1\) , then the curve also passes through the point
- A \(\left( {\frac{1}{3},24} \right)\)
- B \(\left( {\frac{1}{2},4} \right)\)
- C \(\left( {2,\frac{1}{8}} \right)\)
- D \(\left( {3,\frac{1}{28}} \right)\)
Answer & Solution
Correct Answer
(C) \(\left( {2,\frac{1}{8}} \right)\)
Step-by-step Solution
Detailed explanation
\(\left( c \right)\) Let \(y=f(x)\) be acure slope of tangent \(=f'(x)\) Equation of tangent \((Y-y)=f'(x)(X-x)\) Put \(Y=0\) \(X = \left( {x - \frac{y}{{f'\left( x \right)}}} \right)\) Put \(X=0\) \(Y = y - x\,\,\,\,\,f'\left( x \right)\)…
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