JEE Mains · Maths · STD 12 - 6. Application of derivatives
The number of points on the curve \(y=54 x^5-\) \(135 x^4-70 x^3+180 x^2+210 x\) at which the normal lines are parallel to \(x+90 y+2=0\) is :
- A \(2\)
- B \(3\)
- C \(4\)
- D \(0\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
Normal of line is parallel to line \(x+90 y+2=0\) \(m _{ N }=-\frac{1}{90}\) \(-\left(\frac{ dx }{ dy }\right)_{\left(x_1 y_1\right)}=-\frac{1}{90} \Rightarrow\left(\frac{ dy }{ dx }\right)_{\left(x_1 y_1\right)}=90\) Now, \(\frac{d y}{d x}=270 x^4-540 x^3-210 x^2+360 x+210=90\)…
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