Question

If tangent at any point of the curve y = x³ + lx² + x + 5 makes acute angle with x-axis, then –

• A. 0 <l< 3
• B. – $\sqrt{3}$<l<$\sqrt{3}$
• C. |l| < 1
• D. lĪ (0, 1)

Answer 1

Answer: (B)

– $\sqrt{3}$<l<$\sqrt{3}$

Answer 2

acute angle ® 1st quadrant

tan q > 0

$\frac{dy}{dx}$ > 0 Ž 3x² + 2lx + 1 > 0

Possible for D < 0 Ž 4l² – 12 < 0

l² – 3 < 0 Ž (l – $\sqrt{3}$) (l + $\sqrt{3}$) < 0

Ž$\begin{matrix}

• \sqrt{3} < \lambda < \sqrt{3} \end{matrix}$