JEE Mains · Maths · STD 12 - 6. Application of derivatives
Which of the following points lies on the tangent to the curve \(x^{4} e^{y}+2 \sqrt{y+1}=3\) at the point \((1,0) ?\)
- A \((2,2)\)
- B \((-2,6)\)
- C \((-2,4)\)
- D \((2,6)\)
Answer & Solution
Correct Answer
(B) \((-2,6)\)
Step-by-step Solution
Detailed explanation
\(x^{4} e^{y}+2 \sqrt{y+1}=3\) d.w.r. to \(x\) \(x^{4} e^{y} y^{\prime}+e^{y} 4 x^{3}+\frac{2 y^{\prime}}{2 \sqrt{y+1}}=0\) at \(P (1,0)\) \(y _{ P }^{\prime}+4+ y _{ P }^{\prime}=0\) \(\Rightarrow y _{ P }^{\prime}=-2\) Tangent at \(P (1,0)\) is \(y-0=-2(x-1)\) \(2 x+y=2\)…
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