AP EAMCET · Maths · Application of Derivatives
If the tangent drawn at the point \(\left(\mathrm{x}_1, \mathrm{y}_1\right), \mathrm{x}_1, \mathrm{y}_1 \in \mathrm{~N}\) on the curve \(y=x^4-2 x^3+x^2+5 x\) passes through origin, then \(x_1+y_1=\)
- A 5
- B 4
- C 7
- D 6
Answer & Solution
Correct Answer
(D) 6
Step-by-step Solution
Detailed explanation
\( \frac{dy}{dx} = 4x^3-6x^2+2x+5 \) Tangent at \( (\mathrm{x}_1, \mathrm{y}_1) \) passes through origin: \( \mathrm{y}_1 = \mathrm{x}_1 \left( 4\mathrm{x}_1^3-6\mathrm{x}_1^2+2\mathrm{x}_1+5 \right) \) Point \( (\mathrm{x}_1, \mathrm{y}_1) \) on curve:…
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