Question

If at each point of the curve y = x³ – ax² + x + 2, the tangent is inclined at an acute angle with the positive direction of x-axis then –

• A. a £ – $\sqrt{3}$ or a ³$\sqrt{3}$
• B. a > 0
• C. – $\sqrt{3}$< a <$\sqrt{3}$
• D. None of these

Answer 1

Answer: (C)

– $\sqrt{3}$< a <$\sqrt{3}$

Answer 2

$\frac{dy}{dx}$ = 3x² – 2ax + 1 > 0

(Q tangent make acute angle \ $\frac{dy}{dx}$ > 0 )

\ D < 0 Ž 4a² – 12 < 0 Ž –$\sqrt{3}$ < a < $\sqrt{3}$