JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the tangent to the curve \(y=x^{3}-x^{2}+x\) at the point \((a, b)\) is also tangent to the curve \(y=5 x^{2}+\) \(2 x -25\) at the point \((2,-1)\), then \(|2 a +9 b |\) is equal to \(........\)
- A \(196\)
- B \(194\)
- C \(195\)
- D \(193\)
Answer & Solution
Correct Answer
(C) \(195\)
Step-by-step Solution
Detailed explanation
\(y=5 x^{2}+2 x-25 \quad P(2,-1)\) \(y^{\prime}=10 x+2\) \(y_{P}^{\prime}=22\) \(\therefore\) tangent to curve at \(P\) \(y+1=22(x-2)\) \(y=22 x-45\) \(y=x^{3}-x^{2}+x\) \(\left.\frac{ dy }{ dx }\right|_{ C _{2}}=3 x ^{2}-2 x +1\)…
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